Heterogeneity, coordination and competition: the distribution of individual preferences in organisations

This paper experimentally investigates how inter- and intragroup heterogeneity (related to individual cooperative preferences) influences intergroup coordination. Coordination incentives are implemented through an intergroup rank-order competition. A pre-competition phase determines how individual heterogeneity is distributed across groups within an organisation. Two treatments are compared: a horizontal-heterogeneity treatment (H-Hetero, baseline), where individual differences are randomly distributed within and between groups, and a vertical-heterogeneity treatment (V-Hetero), in which groups are internally homogeneous but differ considerably from each other. In contrast to expectations, I find that vertical (intergroup) heterogeneity, when being accompanied by intragroup homogeneity, does not reduce the ability of groups to coordinate and keeps overall performance at very high levels. Indeed, subjects react more strongly to the coordination/competition incentives in vertically heterogenous organisations. Further analysis suggests that group dynamics are mainly driven by a positive orientation towards inequality (distributional preferences) of the members of the initially least cooperative groups, and their non-conditional cooperative behaviour. These results have implications for the design of group-based incentives and governance in organisations and societies.


Introduction
The successful functioning of organisations and societies often requires the groups within them to coordinate to achieve efficient outcomes. However, coordination is not always successful. Important coordination problems can arise when the groups that need to coordinate differ considerably from one another. Coordination becomes particularly challenging in firms and organisations that are faced with the need to first promote cooperation within groups and then coordination between groups. In these complex situations, group partnership is central to explain the success of intergroup coordination.
This paper experimentally investigates the role of inter-and intragroup heterogeneity in intergroup coordination. The source of heterogeneity is based on the prosocial preferences of group members. Specifically, an exogenous sorting mechanism is applied to create groups based on the similarity of initial propensities to cooperate. Previous research has shown that assortative matching is one of the most effective non-punitive mechanisms to foster intragroup cooperation (Chaudhuri 2011;Guido et al. 2019), but its effects on intergroup coordination remain unexplored. This paper therefore addresses an important empirical question: are sorted groups more or less able to achieve efficient intergroup coordination than randomly formed groups? A novel laboratory experiment is designed to answer this question under tightly controlled conditions. Intergroup coordination is modelled by means of an intergroup rank-order competition game. This competition game involves providing incentives for groups to coordinate on multiple Pareto-ranked symmetric pure strategy equilibria. The efficient equilibrium consists of all groups contributing at the maximum level, while zero contribution by all groups leads to the worst equilibrium. At any symmetric equilibrium, all groups are top-ranked and win the competition ("all-can-win"). The competitive context captures the essential features of an "equality-of-opportunities" society (not "equality-of-outcomes") at the group level. 1 This is a significant feature for addressing group diversity and social inclusion.
The experiment has two treatments, each of which has three phases. For both treatments, phase 0 consists of eliciting individual cooperative preferences by playing a one-shot public goods game (Gächter and Thöni 2005). In phase 1, participants are grouped into 12-person organisations consisting of four 3-member groups. There are two procedures to form the groups, one for each treatment. Using a fixedmatching protocol, members in each group play a repeated linear public goods game for ten periods. Later, phase 2 introduces a rank-order competition among the four groups that make up each organisation, holding constant the group composition from phase 1 (Reuben and Tyran 2010). At the end of the experiment, a questionnaire is administered to assess another aspect related to preferences: distributional preferences (Singelis et al. 1995).

3
Heterogeneity, coordination and competition: the distribution… The two treatments are conducted in a between-subject design. They differ in the grouping procedure applied at the start of phase 1. In the horizontal-heterogeneity treatment (H-Hetero, hereafter), groups are formed randomly, so that individual heterogeneity is randomly distributed within and between groups. In the vertical-heterogeneity treatment (V-Hetero, hereafter), groups are exogenously created based on the dispositions of individuals to cooperate elicited in phase 0. The sorting mechanism consists of an initial segregation into different groups of high cooperators and low cooperators, which remain fixed during phases 1 and 2. Consequently, intergroup differences are expected to be more salient in V-Hetero than in H-Hetero. The effects of heterogeneity distribution (horizontal or vertical) on intergroup coordination are tested in phase 2, when intergroup competition is introduced, by comparing behaviour between random groups (H-Hetero) and sorted groups (V-Hetero).
The experimental results reveal that vertical heterogeneity does not reduce the ability of groups to coordinate, although a high degree of coordination failure is observed in both treatments. Furthermore, in V-Hetero, competition significantly reduces intergroup differences while maintaining the overall performance at very high levels. Interestingly, two behavioural patterns are observed in relation to initially low cooperators with intergroup competition: (1) they do not respond to the contributions of their group partners in either heterogeneity treatment, and (2) those with strong vertical distributional preferences cooperate more under vertical heterogeneity.
Intergroup coordination has been little studied in previous research. Some studies have suggested that groups may coordinate better than individuals to achieve efficient outcomes (Feri et al. 2010;Chaudhuri et al. 2015). In coordination between groups, the effects of some sources of intragroup heterogeneity, such as the matching protocol (Chaudhuri et al. 2015) or ethnic identities (Morton et al. 2020), have been examined. In general, these studies show that greater heterogeneity between groups can impair intergroup coordination.
This research is also closely linked to the literature on cooperation and competition. On the one hand, experimental evidence on public goods games shows that: (1) repeated interactions between cooperators and would-be free riders within a group are important in explaining the decay in cooperation levels, and (2) many subjects behave as conditional cooperators (see the surveys of Ledyard 1995;Chaudhuri 2011). Sorting mechanisms have shown to be effective in promoting cooperation in the presence of conditional cooperators (Guido et al. 2019). In particular, separating cooperators from free riders to exogenously form homogenous groups can impede the decay in contribution levels (Gächter and Thöni 2005;Burlando and Guala 2005;Ones and Putterman 2007;de Oliveira et al. 2015). On the other hand, it is well documented in the literature on group contests that intergroup competition can be a powerful force for promoting cooperation within groups (Bornstein et al. 2002;Gunnthorsdottir and Rapoport 2006;Tan and Bolle 2007;Puurtinen and Mappes 2009). Sheremeta (2018) provides a comprehensive survey of experimental evidence in group contests. More closely related to this study, research on rank-order competition (with more than two groups) confirms the positive properties of intergroup competition when individuals are randomly assigned to groups (Reuben and Tyran 2010;Markussen et al. 2014;Cárdenas and Mantilla 2015). This paper contributes to the literature in two ways. First, this study advances our understanding of the effect of group diversity on intergroup coordination by investigating the effects of group formation, in particular by comparing random groups (H-Hetero) to groups sorted according to initial pro-social preferences (V-Hetero). The experimental results suggest that vertical heterogeneity (sorted groups) does not hinder group coordination, at least in the strategic context considered in this paper.
Second, this study contributes to the literature on intergroup competition by analysing the effectiveness of an exogenous sorting mechanism in a competitive context. The experimental findings provide novel evidence on: (1) the overall positive effect of competition on cooperation with sorted groups; (2) the intragroup conditional behaviour of initially high cooperators and initially medium cooperators, regardless of the grouping procedure; and (3) the intragroup unconditional behaviour of initially low cooperators, independently of the grouping procedure. Therefore, this research extends the findings of the social dilemmas literature on conditional/unconditional behaviour to competitive contexts.
The remainder of the paper is organised as follows. Section 2 provides a review of the literature. Section 3 presents the experimental design, procedures and research hypotheses. Section 4 reports the main results, which are discussed in Sect. 5. Finally, Sect. 6 concludes the paper. 2 2 Literature review Coordination games, in addition to resembling many relevant real-world situations, address one of the most difficult challenges in game theory: equilibrium selection (Harsanyi and Selten 1988). Most of the experimental research on coordination games has focused on the decisions made by individuals. There is strong evidence for the inability of subjects to achieve efficient coordination (Ochs 1995;Camerer 2003;Devetag and Ortmann 2007;Chaudhuri 2009). More recent attention has focused on the comparative performance of individuals and teams in coordination games. Experimental studies suggest that teams may be more successful at sustaining efficient coordination than individuals (Feri et al. 2010;Chaudhuri et al. 2015).
The main focus of this paper is on the coordination between groups, rather than on the comparative behaviour of individuals and teams. There is a relatively small body of literature that is concerned with intergroup coordination. For instance, Chaudhuri et al. (2015) study group coordination using a minimum effort coordination game. They compare coordinating behaviour with fixed and random re-matching protocols. In their design, there are no restrictions on team decision-making before interacting with other teams. Their results show that when teams are randomly re-matched after each round, teams are worse at coordinating (towards the efficient outcome) compared to teams with fixed matching. Morton et al. (2020), in an experiment conducted in China, examine the effects of identity diversity on intergroup coordination. Participants, paired in groups of two, play a voter coordination game that is a team version of the battle of the sexes game. The authors find that, when combining multiple identities (non-descent based and descent-based), conflicting multiple identities significantly hamper group coordination compared to reinforcing multiple identities. Taken together, these two studies indicate that individual heterogeneity and group composition influence the ability of groups to coordinate. This paper analyses the effects of a source of heterogeneity mostly ignored by other studies, namely the cooperative preferences of individuals. Another difference of this study from previous ones has to do with the coordination game used. Here, the coordination context is modelled by an intergroup rank-order competition with multiple Pareto-ranked equilibria. Coordination is achieved when all groups reach the same level of cooperation. Intragroup interactions are established by a public goods game. Therefore, since an increase in intragroup cooperation automatically leads to a rise in intergroup competition, the discussion is structured by first presenting the main experimental literature on cooperation in public goods games, and then on competition.
In public goods experiments, evidence shows that there are distinct types of players who differ in their social preferences and/or in their beliefs about their fellow players. One of the most notable behavioural patterns is conditional cooperation (see the surveys of Ledyard 1995;Chaudhuri 2011). In contrast to theoretical predictions, many subjects behave as conditional cooperators whose contributions to the public good are positively correlated either with their ex-ante beliefs about the contributions to be made by their group members or with the actual contributions of such group members. 3 The phenomenon of conditional cooperation has been shown to be quite ubiquitous and robust across cultures and the mode of response elicitation (see, for instance, Kurzban and Houser 2005;Burlando and Guala 2005).
Conditional cooperators seem to be highly sensitive to the presence of free riders (self-interested subjects who always contribute zero to the public good). Research indicates that the co-existence of conditional cooperators and free riders within a randomly formed group is important in explaining the decay of contributions over time in repeated public goods games. Several mechanisms have been examined to promote cooperation in public goods experiments. 4 As noted by Chaudhuri (2011), assortative matching is one of the most effective non-punitive mechanisms to foster cooperation in the presence of conditional cooperators. Assortative matching involves forming sorted groups based on similarity of behaviour or preferences. Guido et al. (2019) provide a systematic literature review and a meta-analysis of the sorting methods that have been used to create groups.
There are basically two types of sorting mechanisms: endogenous and exogenous. While endogenous sorting mechanisms allow subjects to enter or leave groups on their own accord, exogenous sorting mechanisms are implemented by the experimenter on the basis of a pre-determined rule that may or may not be known by the participants. This paper focuses on exogenous methods, as this is the kind of mechanism that is applied in this paper. 5 Among the studies applying exogenous grouping mechanisms, some use one-shot games to sort subjects (Gächter and Thöni 2005;de Oliveira et al. 2015), while others use repeated interactions (Burlando and Guala 2005;Gunnthorsdottir et al. 2007;Ones and Putterman 2007;Gunnthorsdottir et al. 2010). It is worth mentioning that Guido et al. (2019) observe that the separation of cooperators from would-be free riders appears to be more successful in games that use one-shot interaction than in games that use repeated interactions.
Two important issues emerge from these studies in repeated linear public goods games: First, cooperation levels among the sorted groups are greater than among random groups. Gunnthorsdottir et al. (2007) apply a re-matching protocol at the end of each round in both grouping rules (random and sorted), while Gächter and Thöni (2005) and Burlando and Guala (2005) keep group composition fixed during repeated interactions. Regardless of matching, exogenous sorting mechanisms lead to a substantial increase in cooperation. Moreover, the contributions of the highest cooperators in the sorted groups exceed the contributions of the highest cooperators in the random groups. Second, cooperative preferences are stable over time. Ones and Putterman (2007) find that early contributions can serve as a significant predictor of contributions in later decisions. This result is also supported by Kurzban and Houser (2005) and Gunnthorsdottir et al. (2007).
In this paper, the one-shot mechanism designed by Gächter and Thöni (2005) (a one-shot public goods game) is applied to elicit cooperative preferences in phase 0. Later, in phase 1, also following Gächter and Thöni (2005), subjects play a repeated linear public goods game under fixed matching, in random groups or sorted groups. However, contrary to Gächter and Thöni (2005), participants in this experiment are not aware of the group composition at any phase in order to avoid strategic behaviour (see Gunnthorsdottir et al. 2007;Burlando and Guala 2005, for a similar informational context). In this regard, de Oliveira et al. (2015) investigate the effect of providing participants with information about the preference types of the other group members, in homogeneous groups and in heterogeneous groups. Their findings show that information about group composition impacts solely on those groups consisting of all cooperators. This suggests that, in addition to the actual presence of 1 3 Heterogeneity, coordination and competition: the distribution… like-minded members, conditional cooperators need to know that there are no selfish types in their group for them to maintain cooperation (see Guido et al. 2019, for further evidence). All of the studies reviewed here support the notion that sorted groups outperform random groups in public goods experiments. However, to the best of my knowledge, there is no experimental evidence on the effect of sorting in group competitions. Below, the main literature on intergroup competition closely related to this paper is reviewed.
There is much experimental literature on contests between individuals and between groups. Most research focuses on a strategic scenario in which two individuals or groups compete to win a contest and receive a prize. The performance of each individual/group determines the probability of winning the contest. Since costly effort is only used for the appropriation of the prize and not for its production, higher effort is viewed as socially wasteful (see the surveys of Dechenaux et al. 2015;Sheremeta 2019). Collectively, two main results can be highlighted from this literature: (1) there is an excessive of effort by subjects, compared to theoretical predictions; and (2) there is a significant heterogeneity of behaviour within and between groups. Some features related to individual heterogeneity (such as nonmonetary utility of winning, bounded rationality or relative payoff maximisation) have been examined to explain such heterogeneity in contests. In most studies, individuals are assigned to groups exogenously and randomly (Sheremeta 2013(Sheremeta , 2018. More specifically, in two-group contests, experimental findings support the idea that intergroup conflict is effective in fostering cooperation/coordination within groups. Some studies have focused on intragroup interactions modelled by social dilemmas (Gunnthorsdottir and Rapoport 2006;Tan and Bolle 2007;Puurtinen and Mappes 2009;Beekman et al. 2017), while others have considered group members tackling a coordination game (Bornstein et al. 2002).
In contrast, the competitive context examined in this paper entails a more realistic situation with more than two groups. In this line of research, Reuben and Tyran (2010) design a rank-order competition between five groups in which all groups can be ranked first by contributing at the same level (everyone can be a winner). It has the advantage that it can eliminate the negative externality that one group's performance imposes on other groups, although it does not eliminate lowcooperation equilibria. The authors find a universal increase in intragroup cooperation. In the same vein, Cárdenas and Mantilla (2015) conduct an experiment with an intragroup cooperation dilemma and intergroup rank-order competition. However, in their design the only symmetric Nash equilibrium is full cooperation. They investigate the informational effects of the relative ranking of individuals within groups and the ranking of an individual's own group relative to other groups. Their findings show a negative effect of group ranking and a positive effect of individual ranking. Similarly, Tan and Bolle (2007) also find a reduction (increase) in intragroup cooperation in response to wins (losses) in finitely repeated intergroup competitions. In a context of voting to adopt competition or not, Markussen et al. (2014) design an experiment in which participants collectively decide whether or not to introduce competition using two electoral rules: absolute majority or group veto. They find that competition is more likely to be chosen under majority rule. Given the foregoing, this paper uses the competition game designed by Reuben and Tyran (2010), as it allows for the exploration of efficiency issues in intergroup coordination. This research takes their competition game and adds a behavioural mechanism based on group sorting.
Finally, regarding sorting procedures, individuals are randomly assigned to groups in all the aforementioned works on competition, and are either randomly re-matched after each round (Gunnthorsdottir and Rapoport 2006;Puurtinen and Mappes 2009) or left in a fixed partnership (Reuben and Tyran 2010;Markussen et al. 2014;Cárdenas and Mantilla 2015). In contrast, this paper aims to compare competitive behaviour between random groups and sorted groups. Based on previous research on cooperation and sorting, notable differences between groups are expected to emerge with sorted groups during the pre-competition phase 1. Then, in phase 2, sorted groups compete against each other under unequal conditions. Looking at the recent experimental literature on group contests (with two groups), it would be reasonable to expect that group sorting can generate detrimental effects in intergroup competitions. Some studies have found negative effects of intergroup differences, such as differences in group size (Abbink et al. 2010), endowments (Heap et al. 2015), costs (Bhattacharya 2016), communication (Cason et al. 2017) and abilities (Fallucchi et al. 2020). However, the role of cooperative attitudes appears not to have been explored previously. This paper makes it possible to test whether sorted groups will be able to overcome their relative disparities and compete for the first rank. If so, the sorted groups will simultaneously have demonstrated their ability to achieve successful coordination.

The experiment
In this section, I first present the intergroup rank-order competition game, then I discuss the experimental design and procedures. Finally, I posit the research hypotheses.

The intergroup rank-order competition
The basic decision situation is a rank-order competition game among four groups. The incentive scheme is built on Reuben and Tyran (2010). Let N = 1, ..., 12 stand for an organisation of 12 individuals who interact in groups of three members each for t = 1, ..., 10 periods according to a fixed matching design. Let k = 1, ..., 4 be each of the four competing groups. At the beginning of any period, each individual i ∈ N in group k is endowed with 20 points ( e ikt ) which he/she can either contribute to a public good (group account) or keep for himself/herself (private account). Let c ikt be i' contribution to the public good k in period t. Therefore, it can be denoted G kt = ∑ 3 j=1 c jkt as the total contribution to the public good k by the three members in t. In each period t = 1, ..., 10 , the monetary payoff of player i (for all i ∈ N ) is given by: where k is a conversion factor which depends on the rank of the group k in t. Notice that the mathematical expression in brackets corresponds to the payoff function in a linear public goods game with a marginal per-capita return equals 0.5. The conversion factor, k , affects both private and public individual earnings.
The conversion factors are set to satisfy two conditions. First, they impose some penalty for the under-performing groups. In particular, k = 1 is given to the firstranked groups; k = 0.75 to the second-ranking; k = 0.5 to the third-ranking; and k = 0.25 to the fourth-ranking. Second, in the case of a tie between two or more groups, all of them share the same rank and, thereby, get the same conversion factor. 6 Therefore, fines can be avoided altogether by all groups exhibiting the same total contributions although, within groups, individuals could be contributing different amounts. This second condition permits establishing an equality-of-opportunities environment in which all groups can be winners.
Given the parameter specification, the intergroup rank-order competition game has multiple symmetric equilibria at the group level, where any outcome G 1 = ⋯ = G 4 constitutes an equilibrium. These equilibria are Pareto-ranked, being G k = 60 , for all k, the Pareto optimal (the full-contribution equilibrium) and G k = 0 , for all k, the least efficient (the full-defection equilibrium). In any of these symmetric equilibria, the four groups would be ranked first, and nobody would be penalised. 7 The chosen incentive scheme imposes strong penalties for miscoordination, particularly costly for groups that deviate negatively from a symmetric equilibrium. In the case of a group's ranking changing from first to fourth, the earnings of all group members are reduced by 75%. 8 In contrast, a positive deviation would not change the ranking of the group that deviates but would impose a reduction of 25% on the earnings of the other groups. This property becomes particularly challenging in organisations with salient intergroup differences, as in the V-Hetero treatment. For instance, those groups entirely formed by high cooperators might not be willing to damage the lower cooperative groups and might accept working at a lower level of group performance. This would be expected if the 12-person organisation was the "reference group" for top cooperators and they did not distinguish between in-group and out-group partners. An alternative incentive scheme is proposed in Cárdenas and Mantilla (2015), with multipliers ( k ) that are used for punishing and rewarding groups simultaneously. Under their design, there is only one symmetric Nash If only two groups reached the top contributions, both would achieve the first rank, and the group(s) with the following total contribution(s) (the second level) would be ranked third. 7 Notice that the equality of opportunities (at the group level) would imply equality of outcomes (at the individual level) only in two situations: the full-contribution equilibrium and the full-defection equilibrium. 8 Assume that all players are in a symmetric equilibrium and, therefore, all groups are ranked first. If player i reduces his/her contribution to zero, his/her group will change from being ranked first to being ranked fourth. He/She will only do so . As 1 = 1 and 4 = 0.25 , there is no incentive for a player to deviate unilaterally downwards. equilibrium given by full contribution. As the main focus of this paper is on coordination problems, I implement an incentive structure with many symmetric Nash equilibria, including the full-defection equilibrium, to examine how intergroup heterogeneity affects coordination among groups. 9 Last, the competition game also has multiple asymmetric equilibria, namely Nash equilibria in which not all groups achieve the same contribution levels. For example, imagine that three groups contribute everything and one group contributes nothing to the public good. In this case, the noncontributing group is ranked fourth and all their members would be penalised 75% . An individual player has no incentive to increase his/her contribution since he/she cannot change the group's ranking by doing so ( This incentive feature is crucial for the purposes of this paper. It may be expected that when intergroup differences are more pronounced, as in the V-Hetero treatment, the frequency of asymmetric Nash equilibria will be higher. Moreover, the most cooperative groups might set contribution levels so high that the least cooperative groups disengage from the competition. In sum, two main conditions are required to achieve successful coordination at the efficient level: (i) the most cooperative groups should behave doggedly and keep their contributions at the maximum level, and (ii) the less cooperative groups should overcome their (within-group) social dilemma and react positively to the (betweengroup) competition incentives. Given that the theoretical predictions are identical for the two treatments, it is an empirical question to study how the type of heterogeneity (within and between groups) determines intergroup coordination success in competitive organisations.

The experimental design
The experiment was divided into three phases (within-subject): (i) phase 0 or the "cooperative preferences elicitation" phase; (ii) phase 1 or the "pre-competition" phase; and (iii) phase 2 or the "competition" phase. The two treatments differ in the grouping rule applied in the beginning of phase 1. For comparability reasons, the instructions were exactly the same in the two treatments. The instructions were read aloud, and the subjects answered several control questions to verify their understanding of the experiment. At the beginning of the experiment, participants were told that there would be different phases and that they would receive the corresponding instructions to be followed when they started each phase. Subjects were not informed about the next phases in order to avoid strategic decisions. As noted by Guido et al. (2019), subjects may behave strategically when they know that their decisions may influence subsequent behaviour of with whom they will be grouped in the next phases. 10 Treatments are conducted in separate sessions (between-subject design).
Phase 0 consisted of playing a one-shot linear public goods game in 3-member groups formed randomly. Each member was endowed with 20 points ( e i ) which he/ she could either keep for himself/herself or contribute to a public good ( c i ). The individual payoff function was given by: The individual contribution to the public good is used to measure initial cooperativeness, that is, individual cooperative preferences (see Gächter and Thöni 2005, for a similar instrument). In phase 1, the pre-competition phase, new groups were constituted. Participants were randomly divided into organisations of 12 people, with four groups of three members each. The procedure used to form the groups differs between treatments. In the H-Hetero treatment, the groups are randomly formed to get a horizontal distribution of cooperative preferences in each organisation. 11 In contrast, in the V-Hetero treatment, the participants are grouped according to their similar cooperative preferences to form organisations with great intergroup disparities. In each organisation, vertical heterogeneity is implemented by forming internally homogeneous groups but very diverse from each other from a cooperation standpoint. In this regard, within each organisation, individual contributions of phase 0 were ordered from the highest to the lowest levels. Groups were formed in the following way: group 1 was composed of the three highest contributors, group 2 was made up of the subjects with the three next highest levels, and so on until the last group, group 4, which was composed of the three lowest contribution levels. Thus, I implement an exogenous method of forming homogeneous groups (likedminded partners) to separate high cooperators from low cooperators into different groups (sorted groups). This method is similar to that of Gächter and Thöni (2005), Burlando and Guala (2005) and de Oliveira et al. (2015), where the formation of groups is based on earlier tasks that participants did not know would influence later groupings. In particular, I use the same one-shot task as Gächter and Thöni (2005) to elicit cooperative attitudes (in phase 0) in an easy and quick way. But, this design differs from Gächter and Thöni (2005) in that participants were not aware of the sorting method. Namely, subjects were not given any information on the matching procedure in either treatment; they only knew that their group partners would remain fixed during the phase. There are other studies implementing similar exogenous sorting mechanisms surveyed in Guido et al. (2019).
During the pre-competition phase, each independent group repeatedly played a public goods game with the payoff function (2) of phase 0 for ten periods. I introduce a pre-competition phase with groups working independently for various reasons: (i) to allow subjects opportunities for social learning about their partners' cooperativeness; (ii) to provide subjects with the opportunity to create their own group identity before interacting with other groups; and, more importantly, (iii) to generate the type of heterogeneity (horizontal and vertical) before introducing intergroup competition.
In phase 2, the competition phase, an intergroup rank-order competition was carried out among the four groups forming each organisation, as previously explained. This phase lasted another ten periods, keeping constant the group composition from phase 1. In most of the public goods studies with intergroup competition, subjects are randomly rematched after each interaction. Here, I follow the approach by Reuben and Tyran (2010), Markussen et al. (2014) and Cárdenas and Mantilla (2015), who hold fixed groups among the competition periods. This paper contributes to this literature by analysing behaviour with sorted groups.
Finally, at the end of the experiment, a questionnaire was administered to participants to obtain information about distributional preferences and some general socio-demographics data. To elicit individual distributional preferences, I use the 32-item scale designed by Singelis et al. (1995) (see "Appendix"). This questionnaire has been used in previous research to measure the degree of vertical and horizontal individualism and collectivism (Oyserman et al. 2002;Taras et al. 2010). 12 Social psychologists (Triandis 1995;Chen et al. 2002;Hofstede et al. 2010), and recently, economists (Hajikhameneh and Kimbrough 2019, and the references therein) have mainly focused on the individualism-collectivism dimensions. The individualism-collectivism dimensions measure the relative importance of freedom/ independence in making decisions within groups. While individualists are selfinterested and autonomous, collectivists are interdependent and pursue the group interest. The vertical-horizontal sub-dimensions measure the relative importance of the value of equality among members of a group. The vertical value recognises and accepts diversity and inequality within group members, while the horizontal value supports the egalitarian status. A series of cross-cultural experiments have suggested the important influence of vertical and horizontal individualism and collectivism in economic decisions (Triandis et al. 2001;Chen and Li 2005;Komarraju et al. 2008;Frank et al. 2015). Therefore, I focus on the vertical-horizontal sub-dimensions to measure individual distributional preferences. 13 It is my interest to connect these types of distributional preferences with behaviour observed in the organisation-level heterogeneity treatments. The closest work to this paper is Probst et al. (1999), which studies the influence of these cultural patterns in social dilemmas (with and without intergroup competition), but not involving inter-and intragroup heterogeneity.

Procedures
The experiment was conducted at the LINEEX laboratory of the University of Valencia. It involved a total of 144 subjects with no prior experience with public goods experiments. 14 All sessions were computerised using the z-tree software (Fischbacher 2007). Average earnings were 23.49 euros (including a 5 euro show up fee) from a minimum of 14 euros to a maximum of 32.7 euros. Payoffs were accumulated over the three phases (21 rounds), and participants were paid individually and privately at the end of the experimental session, using an exchange rate of 1 euro per 20 points. The sessions lasted approximately 90 minutes.
Under a between-subject design, there were 60 subjects in the H-Hetero treatment (one session) and 84 subjects in the V-Hetero treatment (two sessions, 60 and 24 subjects). In each session, subjects were assigned to organisations formed by four groups of three members each. Therefore, there were 20 groups in H-Hetero (five organisations) and 28 groups in V-Hetero (seven organisations). 15 After each round, subjects received feedback on their group's total contribution, individual earnings and, additionally for the competition phase, total contributions of all groups, ranking of groups and conversion factors.

Hypotheses
The main hypothesis is posited regarding the impact of H/V heterogeneity on intergroup coordination success. Even though research on public goods has provided strong support for the effectiveness of sorting methods in enhancing overall performance when groups are independent (Burlando and Guala 2005;Ones and Putterman 2007;de Oliveira et al. 2015), group sorting procedures also generate considerable differences among group performances. When intergroup interactions are introduced, prior intergroup diversity may make coordination among groups more challenging. Research on coordination games with multiple Pareto-ranked equilibria shows that, despite groups coordinating more successfully than individuals, the degree of coordination failure observed among groups is still considerably high (Feri et al. 2010;Chaudhuri et al. 2015). Here, I am not interested in the comparative performance between individuals and groups, however. By focusing just on groups, Chaudhuri et al. (2015) find that groups with random matching are worse 14 Of the 144 participants, 59.03% were women (85 out of 144) and 40.97% men (59 out of 144), and the average age was 23.24 years old. Most of the subjects were undergraduate students from different disciplines (97 out of 144). The rest were mainly students at the Master's/Doctorate level (20 out of 144) and at the higher vocational training level (15 out of 144). 15 The sample size of 144 subjects was determined with a power analysis. The sample size was first calculated for the case of one sample. Based on previous works, I assume values of contribution under the null and alternative hypotheses of 9 and 11 respectively, a standard deviation of 5 and the standard values of = 0.05 and power test 0.8. This sample size was 39 subjects. Then, the sample sizes inflated by a group cluster factor were determined: 55 subjects in the H-Hetero treatment (assuming = 0.2 , for modest intergroup differences) and 78 subjects in the V-Hetero treatment (assuming = 0.5 , for greater intergroup differences). Then, to attain the desired power, the sample sizes chosen for the experiment were 60 subjects in H-Hetero and 84 subjects in V-Hetero.
at coordinating compared to groups with fixed matching. The literature has not yet addressed coordination success or failure of groups by comparing different types of (fixed) group partnerships. As far as I am concerned, this paper is the first to deal with this issue.
In the competitive coordination game studied in this paper, members of each group simultaneously face an intragroup social dilemma and an intergroup competition. Experimental research on competition games shows that intergroup differences may generate some disengagement effects. Recent works on contests find a negative impact of intergroup differences on overall performance (see for instance Abbink et al. 2010;Heap et al. 2015;Bhattacharya 2016;Cason et al. 2017;Fallucchi et al. 2020). 16 Since intergroup differences should emerge when groups are sorted, it could be expected that groups will find it more difficult to coordinate with each other under vertical heterogeneity. Therefore, I anticipate that:

Hypothesis 1
The coordination level will be lower with vertical heterogeneity than with horizontal heterogeneity. Moreover, coordination at the efficient outcome will be less successful with vertical heterogeneity. I next postulate behavioural hypotheses about the effects of H/V heterogeneity on group behaviour and individual preference types (cooperative and distributional).
The role of H/V heterogeneity for group ranking distributions At the group level, a primary question is whether the salience of intergroup differences will affect the distribution of group rankings when competition is introduced. With horizontal heterogeneity across groups, experimental evidence shows that competition changes the distribution of rankings considerably, with a notable increase in the number of groups attaining the first rank (Reuben and Tyran 2010;Cárdenas and Mantilla 2015). By contrast, with vertical intergroup heterogeneity, I postulate that it will be more challenging for the less cooperative groups to reach high positions during the competition. The groups with higher rankings will be those whose members are more cooperative than members of the other competing groups. In the kind of competition considered in this paper, pro-social individuals do not have motivations to stop contributing to their group due to the lack of negative externalities of their own group's performance on the other groups' earnings. In this treatment, competition incentives could lead to a higher frequency of asymmetric equilibria.
Hence, the second prediction is: Hypothesis 2 The number of first-ranked groups will be lower with vertical heterogeneity than with horizontal heterogeneity.

The role of H/V heterogeneity for individual cooperative preferences
Previous research does not support a consistent relationship between cooperative and competitive behaviour. Experimental evidence provides mixed results. For instance, Savikhin and Sheremeta (2013) observe a negative correlation in contests, whereas Reuben and Tyran (2010) does not find any connection to intergroup rank-order competitions (all players increase their contributions).
In this experiment, subjects acquire some group experience during the precompetition phase. In this regard, group membership might modulate individual reactions to competition. Theoretically, in the competition game, a member of a noncooperative group has no incentive to unilaterally contribute more to achieve a higher rank for the group. In contrast, a member of a highly cooperative group faces clear incentives to keep contributions at high levels. Thus, it could be expected that, in vertical-heterogeneity organisations, the types of individual cooperative preferences will remain the same with and without competition. However, in horizontal-heterogeneity organisations, it is expected similar results to those obtained by Reuben and Tyran (2010): all subjects would contribute more with competition regardless of their cooperative preferences and group membership. Recall that the types of cooperative preferences are defined as the individual contribution levels to the group account.
Hypothesis 3 With vertical heterogeneity, competition will hold the same relative positions of cooperative preference types as those reached during the pre-competition phase. In contrast, competition will change the distribution of cooperative preferences with horizontal heterogeneity.

The role of H/V heterogeneity for individual distributional preferences
To evaluate the heterogeneity effects, attention is focused on vertical-horizontal sub-dimensions of individualism and collectivism (Singelis et al. 1995;Triandis et al. 2001;Chen and Li 2005;Komarraju et al. 2008;Frank et al. 2015). These elements measure the relative importance of the value of equality among members of a group. Therefore, I will consider that these sub-dimensions reflect two different types of distributional preferences of the subjects. Previous experimental work has shown the importance of distinguishing between vertical and horizontal sub-dimensions to explain individual cooperation in social dilemmas (Chen and Li 2005;Probst et al. 1999). In particular, Probst et al. (1999) found significant effects in two types of dilemma (with and without intergroup competition) for the vertical individualists and collectivists, but not for the horizontal ones.
Based on this evidence, in this experiment it is expected that H/V heterogeneity will have a higher incidence on the vertical distributional preferences than on the horizontal ones. Moreover, subjects with vertical distributional preferences will react more strongly to the competition incentives in the vertical-heterogeneity organisations, where the intergroup differences are more salient. Therefore, I postulate the following: Hypothesis 4 Vertical distributional preferences will impact more positively on individual contributions in vertical-heterogeneity organisations than in horizontalheterogeneity organisations.

Results
This section is divided into three parts. First, the heterogeneity effects on coordination and group behaviour will be analysed. Second, the role of heterogeneity on individual preferences (cooperative and distributional) will be evaluated. Last, efficiency issues will be examined. Table 1 presents an overview of the main results. 17 Behaviour observed in the pre-competition phase is consistent with previous research on public goods experiments. First, there is the typical decay in group contributions over time in the H-Hetero treatment. Second, there is an increase in overall performance in V-Hetero compared to H-Hetero (on average, 6.71 versus 5.11 at the individual level; 20.12 versus 15.35 at the group level) (Burlando and Guala 2005;Gächter and Thöni 2005;Ones and Putterman 2007). 18 Third, and more importantly for the purposes of this design, there exists a ranking in group performances in V-Hetero (from the highest to the lowest contribution levels) which persists during the whole phase. As expected, in the V-Hetero treatment intragroup interactions among like-minded members reinforce their initial cooperativeness (elicited in phase 0) and lead eventually to salient intergroup differences, which are not observed in H-Hetero. 19 When intergroup competition is introduced, on average, the individual contribution levels increase considerably in both treatments: in H-Hetero, a striking increase of 220.9% (from 5.11 to 16.40), and in V-Hetero a rise of 241.3% (from 6.71 to 16.91). 20 The median contribution goes from 2 to 20 in H-Hetero and from 5 to 20 in V-Hetero. Furthermore, competition noticeably reduces the higher dispersion 17 Recall that, in the V-Hetero treatment, group 1 consists of the highest cooperators, group 2 of the second highest cooperators, and so on, according to the design features. 18 However, there are no significant differences between treatments. A two-sample Kolmogorov-Smirnov test for equality of distribution functions gives a p = 0.536 at the group level for the whole Phase 1 (Panel B: 48 independent observations, 20 in H-Hetero and 28 in V-Hetero). 19 Notice that initial contributions in Phase 0 are slightly higher in H-Hetero than in H-Vetero, in spite of random assignment of subjects to treatments (see Panels A and B). However, such differences are not significant. Two-sample Kolmogorov-Smirnov tests give a p = 0.318 at the individual level (Panel A: 144 independent observations, 60 in H-Hetero and 84 in V-Hetero), and a p = 0.617 at the group level (Panel B: 48 independent observations, 20 in H-Hetero and 28 in V-Hetero). 20 Wilcoxon matched pairs signed-rank tests at the group level confirm that the increase in contributions is statistically significant in both treatments ( p < 0.001).

3
Heterogeneity, coordination and competition: the distribution… of contributions among groups in V-Hetero, compared to H-Hetero. 21 The treatment H-Hetero replicates the main results obtained by Reuben and Tyran (2010), as expected.
As a first outstanding result, I find that vertical heterogeneity does not negatively affect coordination across groups, at least compared to horizontal heterogeneity. Despite the salient intergroup disparities in V-Hetero, groups show similar data in the amount of miscoordination to H-Hetero. Panel D of Table 1 presents five different indicators for this statement. Miscoord. Degree is measured as the average of the relative difference between the sum of groups' rankings and the sum of groups' rankings when there is perfect coordination (i.e., 4) in the same period. This indicator is slightly lower in V-Hetero than in H-Hetero (1.26 vs. 1.30). Moreover, by comparing the proportion of times in which miscoordination entails two levels of group rankings (Two-ranks Miscoord., 2nd column), three levels (Three-ranks Miscoord., 3rd column) or four levels (Four-ranks Miscoord., 4th column) across treatments, I do find that, in V-Hetero, these indicators are larger for the miscoordination levels with 2 ranks (17.14% vs. 12%) and 3 ranks (45.71% vs. 42%) and lower for the level with 4 ranks (37.14% vs. 46%). This result suggests a reduction in the miscoordination degree at the greatest level in V-Hetero compared to H-Hetero. Last, the Adjustment indicator is defined as the average of the absolute difference between a group's own contribution and the maximum group contribution in the previous period. Table 1 shows that there is always less "adjustment" (closer to the first-ranked group) going on in the V-Hetero treatment (6.52 vs. 9.22), implying that groups attempt to settle more quickly in an equilibrium. In all five indicators, I do not find significant differences between both treatments. 22 It is worth mentioning that, despite the "all-canwin" incentives, perfect coordination (with all groups reaching the same total contribution level) is not achieved in any treatment along the ten periods of competition. Therefore, the findings do not provide support for Hypothesis 1.
Result 1 Vertical heterogeneity does not reduce coordinating behaviour as compared to horizontal heterogeneity. In vertically heterogeneous organisations, the competing groups are as successful at avoiding miscoordination as the groups competing in horizontally heterogeneous organisations.
To better understand the behavioural determinants explaining (mis)coordination, I analyse contributions at the group and individual levels with and without intergroup competition. The left panel in Fig. 1 plots the distribution of group rankings 21 From the pre-competition phase to the competition phase, the standard deviation of the group contribution decreases from 6.63 to 5.65 in H-Hetero, and from 7.11 to 4.94 in V-Hetero. Variance ratio one-sided tests at the group level give the following results: p = 0.453 in H-Hetero and p < 0.001 in V-Hetero. 22 The results of two-sample Kolmogorov-Smirnov tests at the organisation level are as follows: p = 0.971 for Miscoord. Degree; p = 0.936 for Two-ranks Miscoord.; p = 1.000 for Three-ranks Miscoord.; p = 0.658 for Four-ranks Miscoord., and p = 0.739 for Adjustment.
with and without competition in the V-Hetero treatment. 23 The width of the bars represents the proportion of times (over all periods) that a group type (numbered from 1 to 4 into each organisation) reaches a particular rank (from first to fourth position). Table 1 Main results Panel D. Miscoord. Degree is defined as the average of the relative difference between the sum of groups' rankings and 4 (the perfect coordination case, where all four groups reach the first rank) in the same period. Adjustment is defined as the average of the absolute difference between a group's own contribution and the maximum group in the previous period As seen, in the V-Hetero treatment, groups react to the competition incentives following an organised pattern: 24 the group formed by the highest cooperators, group 1, reaches the top position most often with and without competition. Surprisingly, the strongest positive reaction to the competition incentives corresponds to group 4, which is mostly ranked at the bottom without competition. Consequently, with intergroup competition, the first ranking is mainly achieved by the two most extreme groups (the highest cooperators and the lowest cooperators), whereas groups 2 and 3 place on lower positions most of the time. The right panel in Fig. 1 illustrates the evolution of the mean ranking achieved by each group type during the competition phase. This riveting picture sheds insights on the effects of vertical heterogeneity on competitive group behaviour. In V-Hetero, the groups seem to have paired off with a partner to compete against each other. Namely, during the second half of the competition phase, two matching competitions appear to emerge: one between groups 1 and 4, and another between groups 2 and 3. Notice how group 4 starts the competition phase at the bottom contribution levels and gradually gains in position up to match the top group 1.
Overall, the number of first-ranked groups is larger in V-Hetero than in H-Hetero. In an average period with competition, 1.4 groups are ranked first in H-Hetero and Econometric analysis confirms previous statements. Tobit panel models with random effects and censured at two limits (0 and 20) are used. I first test for treatment effects with and without competition. Pooling data from the two treatments together, I regress individual contributions on the following explanatory variables: Period, which represents the round of play (from 1 to 10 in every phase); Treatment, a dummy variable with value 1 for V-Hetero and 0 otherwise; and Prev. Others' Contrib., which defines the total contribution of the other two members of the same group in the earlier period. This last variable captures the reciprocity effect commonly found in public goods games (Chaudhuri 2011). Estimations indicate significant treatment effects and a significant decay in contributions, just without competition. However, conditional cooperation is highly significant regardless of the competition conditions. 25 , 26 Table 2 presents estimations for the behavioural determinants of individual contributions across heterogeneity and competition conditions. 27 Estimations support the existence of significant intergroup differences in V-Hetero without competition but not with competition (see the coefficient of Group Type). Looking at intragroup interactions, Prev. Others' Contrib., there are positive and significant reciprocity effects under all conditions, although the greatest effect is observed in pre-competition V-Hetero. Regarding intergroup reactions, Prev. MaxGroup's Contrib, there are only significantly positive effects in V-Hetero. Notice that in this treatment, the impact of group partner contributions is slightly reduced with respect to that observed without competition. However, the influence of other groups' behaviour is very intense and significant. In the next subsection, I will further examine the behavioural reactions across types of cooperative preferences. Last, there exists a significant decay in contributions in the two treatments during the pre-competition 25 Estimations give the following results: (i) a significant decreasing time trend without competition (the coefficient of Period is − 0.87 , p < 0.001 , without competition, and 0.08, p = 0.455 , with competition); (ii) a significant treatment effect without competition (the coefficient of Treatment is 3.14, p = 0.031 , with competition and 1.25, p = 0.468 , without competition); and (iii) a significant reciprocity effect with and without competition (the coefficient of Prev. Others' Contrib. is 0.31 without competition and 0.28 with competition, p < 0.001 in both cases). 26 Data contains a large accumulation of observations at the minimum and at the maximum possible contributions (0 and 20). To consider the consequences of disregarding the censoring, panel data models are estimated with random effects and cluster standard errors adjusted at the group level. The important point is that the coefficients are seriously under-estimated if the censoring at 0 and 20 is not taken into account. For example, the estimate of the Treatment parameter is 1.47 ( p = 0.028 ) in phase 2, which is almost 50% lower than the estimate of 3.14 obtained from the Tobit regression. Similar results are obtained by clustering standard errors at the organisation level. 27 Three new explanatory variables are included: First Period Contrib., the individual contribution to the group account in the first period, to control for individual unobservable heterogeneity along time; Group Type, which defines the group type within an organisation, from 1 to 4, considered just for V-Hetero; and, Prev. MaxGroup's Contrib, the total contribution of the first-ranked group in the previous period, to measure the immediate reactions of individuals to the relative positions of their non-first-ranked group.
To avoid multicollinearity problems, in Table 2, I have dropped those individual observations belonging to a first-ranking group in the previous period.

3
Heterogeneity, coordination and competition: the distribution… phase (higher in H-Hetero than in V-Hetero, as expected) which is not observed in the competition phase. It should be noted that initial contributions, First Period Contrib., are significant in all models.
The experimental findings are summarised in the second result: Result 2 Intergroup rank-order competition is effective in promoting individual contributions with vertical heterogeneity. In vertically heterogeneous organisations, competition significantly reduces the intergroup differences and leads to a systematic re-ordering in the initial group rankings. The first-rank position is more often reached by the highest cooperator groups and the lowest cooperator groups.
Therefore, this result does not provide support for Hypothesis 2.

Heterogeneity and individual preferences
Here, I analyse the relationship between H/V heterogeneity and individual preferences. In particular, two types of preferences are measured: cooperative and distributional. I classify the types of cooperative preferences into three categories: high cooperators (high type), medium cooperators (medium type) and low cooperators (low type). 28 Figure 2 displays the temporal patterns of average contributions across cooperative preference types and competition conditions in the two treatments. As seen, there are remarkably lasting differences between types of economic preferences in V-Hetero during the pre-competition phase. However, intergroup competition changes considerably the relative performances of cooperative preference types. In particular, the low-type position depends crucially on H/V heterogeneity: low cooperators behave more similar to medium cooperators in H-Hetero, while low cooperators move gradually from the medium level to the high level with vertical heterogeneity.
To examine the impact of intergroup competition across cooperative preference types in each treatment, I compute the changes in individual contribution levels as the difference between the contribution to the group account of an individual in a period with competition and her/his contribution in the equivalent period without competition. Table 3 presents the estimations of a Tobit regression model where Treatment is a dummy variable with value 1 for the V-Hetero treatment, while Medium and Low are dummies for medium cooperators and low cooperators, respectively. As shown, there are significant treatment effects for every preference type. Notice that the main effect of Treatment measures only the effect of competition for high cooperators, since interactions between Treatment and Medium/Low types are included in the regression. In this regard, the negative and significant coefficient of Treatment indicates that the positive reaction of high cooperators to competition incentives is significantly lower in V-Hetero than in H-Hetero. As expected, in V-Hetero, the high cooperators increase their contributions to a lesser extent with competition because they already contribute at a very high level in the pre-competition phase. Moreover, there are significant interaction effects between treatment and preference types. In V-Hetero, the medium cooperators and the low cooperators react more positively to the competition incentives (taking high cooperators as the reference type). This is consistent with previous research providing a negative correlation between cooperativeness and competitiveness in contests (Savikhin and Sheremeta 2013).
Therefore, contrary to Hypothesis 3, with vertical heterogeneity, the type of cooperative preferences is not a good predictor for relative cooperative behaviour with competition. This yields the third result: Result 3 Intergroup competition changes considerably the relative performances across cooperative preferences regardless of heterogeneity distribution. More importantly, individuals react more strongly to the competition incentives with vertical heterogeneity, particularly the medium cooperators and the low cooperators.
Last, to deepen understanding of behaviour of the players with different preferences, I investigate the conditionally cooperative behaviours of different types of cooperative preferences in response to the behaviour of their group members as well as the behaviours of other groups. Furthermore, I incorporate the role of individual distributional preferences in the analysis (see "Appendix" for a detailed explanation).
To test Hypothesis 4, each individual is classified according to her/his score on the vertical feature of distributional preferences, Ineq-Pref. The higher the score, the greater the degree of acceptance of inequality among members of an organisation or Heterogeneity, coordination and competition: the distribution… group. 29 In this regard, I measure vertical distributional preferences with a dummy variable, which takes 1 if an individual is high in that variable, and 0 otherwise. An individual is considered to be high in the vertical factor if the mean score of the 16 items used to measure that factor is higher than or equal to the overall mean of all subjects in that factor. Likewise, I also measured the individual score on the horizontal feature of distributional preferences. However, I have not found any significant effects of horizontal distributional preferences under any conditions and, thereby, these results have not been included in the present analysis. Table 4 presents the Tobit panel regressions for conditional behaviour of the three types of cooperative preferences in the competition phase. I have included the Prev. OtherGroups variable, defined as the average total contribution of the other three competing groups in the previous period, to capture the impact of other groups' behaviour. As a whole, I find that group behaviour depends on the interaction between cooperative preferences and distributional preferences.

Fig. 2 Evolution of mean contribution across types of cooperative preferences by treatment and phase
The most relevant results are obtained for low cooperators. First, while high and medium types behave as strong reciprocators by conditioning their contribution on their group partners' contributions, low types do not respond to their group partners' behaviour. This is true in both treatments. This finding extends the conditional behaviour of different types of players commonly observed in the literature on public goods to a strategic setting of intergroup competition (Chaudhuri 2011). The fact that the low cooperators do not respond to the contributions of their partners may suggest that they have standard "homo economicus" preferences. Namely, as egoistic payoff maximisers, they realise that making a high contribution might be individually rational in a rank-order competition in order to increase their own group's rank, since the other groups fail to perfectly coordinate on high contributions. In this regard, it could be argued that the stronger reaction of low cooperators to competition may be because they contribute less in V-Hetero than H-Hetero in phase 1, rather than their contributions are higher in V-Hetero than H-Hetero in phase 2. However, this interpretation is not supported by data. A two-sample Wilcoxon test for equality of low cooperators' contributions in period 1 of phase 1, at the individual level, indicates that there are no significant differences between treatments ( p = 0.4118 ). Furthermore, in Appendix, Table 5 shows the mean contribution levels for each cooperative preference type across treatments and phases. Based on Tobit panel data regressions of individual contributions on Period and Treatment variables, Table 5 also provides the p-values of the corresponding coefficients of Treatment. As shown, behaviour of low cooperators does not differ significantly between treatments in the pre-competition phase. The only significant differences are found for high cooperators. Second, with vertical heterogeneity, I find significantly positive effects of vertical distributional preferences in the sense that those low cooperators who are more willing to accept inequality react more positively to competition incentives. Notice that distributional preferences are measured using the mean score for vertical individualism 30 and vertical collectivism 31 (16 items in total, see "Appendix"). This implies that a high willingness to accept inequality can be interpreted as a strong preference for either being the winner of a competition (individualist view) or sacrificing for the benefit of the group (collectivist view). In both cases, inequality among group members is individually accepted. Therefore, in this experiment, the competition incentives may promote the two kinds of individual behaviour since choosing a high contribution might increase the own group's rank, which responds to both self and group interests.
The following result summarises the findings and is supportive of hypothesis 4: Result 4 With intergroup competition, reciprocity among group members is observed for high cooperators and medium cooperators in both heterogeneity treatments. However, low cooperators do not react to their group partners' behaviour. Moreover, low cooperators with distributional preferences supporting inequality are more competitive in vertical-heterogeneity organisations. 30 The 8 items used to measure vertical individualism are: It annoys me when other people perform better than I do; Competition is the law of nature; When another person does better than I do, I get tense and aroused; Without competition, it is not possible to have a good society; Winning is everything; It is important that I do my job better than others; I enjoy working in situations involving competition with others; Some people emphasize winning; I'm not one of them. 31 The 8 items used to measure vertical collectivism are: I would sacrifice an activity that I enjoy very much if my family did not approve of it; I would do what would please my family, even if I detested that activity; Before taking a major trip, I consult with most members of my family and many friends; I usually sacrifice my self-interest for the benefit of my group; Children should be taught to place duty before pleasure; I hate to disagree with others in my group; We should keep our aging parents with us at home; Children should feel honored if their parents receive a distinguished award.

Heterogeneity and efficiency
Here, I study the implications of H/V heterogeneity for efficiency. As conservative measure of efficiency, I calculate the effective earnings of participants treating sanctions as waste. In aggregate terms, average individual earnings decrease when intergroup competition is introduced in both treatments: from 22.56 to 19.42 in H-Hetero and from 23.35 to 19.90 in V-Hetero (see Panel E in Table 1). If I compare individual earnings of the competition phase to those of the pre-competition phase, I find notable differential patterns across cooperative preferences and distributional preferences. In "Appendix", Figs. 5 and 6 display, for the two treatments, the average earnings for periods with competition (as a percentage of earnings in the equivalent period without competition) across cooperative preferences and distributional preferences, respectively (see also Table 7 in "Appendix").
Regarding cooperative preferences, the most beneficial effect of competition falls on the low cooperators in V-Hetero. In this treatment, their competition earnings considerably surpass pre-competition earnings in the second-half of the time spam (121.29, on average). While low cooperators' relative earnings are approximately the same as those of medium cooperators in H-Hetero, in V-Hetero low cooperators behave more successfully. Estimations based on panel data models with random effects and clustered at group level confirm these results. 32 With respect to distributional preferences, less dispersion in earnings is obtained in V-Hetero than in H-Hetero. In H-Hetero, the participants with weak preferences towards inequality (dashed lines in Fig. 6) achieve higher gains than the participants with strong pro-inequality preferences (107.31 versus 85.84 respectively, in the last five periods). However, in V-Hetero, the dynamics of relative earnings do not differ between distributional preference types, being the pro-inequality individuals who gain higher relative earnings (90.80 versus 96.66 in the last five periods). Panel data regressions support these results.
The following result summarises the findings: Result 5 Despite intergroup competition reduces overall individual earnings in both treatments, there are significant distributive effects that differ across treatments. While high cooperators are the ones who earn more with horizontal heterogeneity, with vertical heterogeneity low cooperators are the most successful. Furthermore, when comparing between distributional preference types, earning inequality is lower in vertically heterogeneous organisations.

3
Heterogeneity, coordination and competition: the distribution…

Discussion
The main objective of this paper has been to examine the impact of the distribution of individual heterogeneity (inter-and intragroup) on intergroup coordination. The incentive system used to analyse the coordination problems has been an intergroup rank-order competition with embedded intragroup social dilemmas. The experimental findings contribute to the literature in three ways. First, this research contributes to the studies on coordination among groups. Research has identified many factors that facilitate efficient coordination among individuals in firms and organisations (Ochs 1995;Devetag and Ortmann 2007). The literature has put particular emphasis on financial incentives, communication, group size, feedback effects or matching effects. Bornstein et al. (2002) discuss how competition between groups enhances coordination within groups. More recently, researchers have studied the ability of teams to coordinate internally at first, and then coordinate across them (Feri et al. 2010;Chaudhuri et al. 2015). Here, I have considered a competitive coordination game among groups where the group contribution levels determine the relative group rankings in an intergroup competition. The findings provide relevant evidence of the role of individual (inter-and intragroup) heterogeneity for intragroup cooperation and intergroup coordination. Despite the high degree of coordination failure observed in both treatments, I have found that, with vertical heterogeneity, groups are as successful at avoiding miscoordination as the groups with horizontal heterogeneity. With repeated interactions, miscoordination is reduced (although differences are statistically insignificant). These results may be explained by the fact that the two treatments differ not only in terms of intergroup heterogeneity but also in terms on intragroup heterogeneity. In the V-Hetero treatment, groups start the competition phase with prior experiences of more homogenous intragroup behavior (in the pre-competition phase), compared to those groups in the H-Hetero treatment. This may make it easier for groups in the V-Hetero treatment to coordinate on increasing contributions in the competition phase. Most likely, fewer participants in V-Hetero experienced being free ridden in the pre-competition phase and, thereby, more people would be willing to contribute so that their group coordinated on high levels under competition incentives. Indeed, rank-order intergroup competition significantly promotes intragroup cooperation regardless of the type of heterogeneity.
Second, this experimental evidence sheds light on the role of individual heterogeneity in intergroup competitions. Previous research on intergroup competition has mainly examined interactions between randomly formed groups, i.e., between similar groups. However, this paper has aimed at the effects of salient intergroup differences in group performances. The experimental results have shown that rank-order competition is particularly successful when it exhibits two desirable properties: i) the most cooperative groups keep their contributions at very high levels, and ii) the least cooperative groups are strongly encouraged to raise their contributions up to compete against the top cooperators. The overall positive effect of competition shown by Reuben and Tyran (2010) with random groups was also replicated for sorted groups. Additionally, this research provides strong support for the effectiveness of competition in reducing intergroup disparities within vertically heterogeneous organisations.
A third contribution of this paper is its practical implication for organisational design and policy design. Given the increasing diversity in organisations and society, designers and policymakers should care about heterogeneity among members as it may hamper overall performance. Some mechanisms have been proposed by prior research, such as segregation of selfish individuals from cooperators (with the subsequent decay of contributions by under-performing groups) or punishment to the low-performing members (see, for example, de Oliveira et al. 2015;Gächter and Thöni 2005). Nevertheless, some organisations cannot afford for any projects to fail when global success depends on all existing groups, or it may be excessively costly to dismiss the least cooperative groups. To be more efficient in socially diverse organisations, the results of this experiment suggest that intergroup competition can be an "integrating" institution of the least performing members under an equality-of-opportunities framework. In this regard, the policymaker should promote intergroup competition in vertically diverse organisations, or even in diverse inter-organisational networks (see also Godoy et al. (2015) for other design features with important policy implications). Furthermore, individual orientations towards inequality may play an important role in the more diverse organisations. The evidence shown in this paper suggests that vertical distributional preferences may promote competition in vertically heterogeneous societies compared to those that are horizontal. Consistent with Balafoutas et al. (2012), distributional preferences seem to be determinant for understanding competitive behaviour. Therefore, the fact that both types of individual preferences (cooperative and distributional) may capture different aspects of group behaviour is in line with Becker et al. (2012).

Concluding remarks
There are many features which can affect coordination among groups integrating an organisation or society. Some of them are defined at the organisational level, such as competition incentives, some are established at the group level, such as inter-and intragroup heterogeneity, while others have a more individual and subjective nature, such as preferences (cooperative and distributional). An assessment of the relative influence of these features and their interactions has been the focus of this research. To the best of my knowledge, this is the first study with that aim.
Intergroup or vertical heterogeneity, when being accompanied by intragroup homogeneity, does not reduce the ability of groups to coordinate. Using an intergroup rank-order competition as coordinating system, its most beneficial effects in terms of organisational performance and relative group performances have been found in vertically heterogeneous organisations.
Regarding intragroup dynamics, conditional cooperation or reciprocity is the primary behavioural pattern, except for the initially least cooperators. Surprisingly, I find that in vertically heterogeneous organisations, the initially least contributing groups reach the first ranking as often as the initially top contributing groups, once intergroup competition is introduced. An internal source seems to explain the strongly competitive behaviour of the lowest groups: the inequality-oriented distributional preferences of their members. Alternatively, it may be that the initially low cooperators have standard "homo economicus" preferences, which are more strongly triggered with vertical heterogeneity. A better understanding of these interesting behavioural patterns may provide fruitful directions for future research.
I believe that experimental analysis aimed at understanding the factors that might influence intergroup coordination is extremely important since coordination problems are ubiquitous in economics and society. This paper is just one step in this direction, but many aspects merit future research, for instance, the role of other socioeconomic sources of organisational diversity such as ethnic identities, gender and social status (Morton et al. 2020;Schram et al. 2019). It would also be interesting to explore the impact of risks on intergroup coordination in heterogeneous organisations. Previous experimental literature points out that subjects cooperate less when facing individual risks than when facing common risks in public goods (Zhang 2019). It is an unexplored question whether diverse groups facing individual versus common risks will be able to coordinate for the success of an organisation or society.

Additional analysis
Cooperative preference types See Table 5.

Factorial analysis of distributional preferences
Based on previous research, the cultural dimensions are first defined with respect to vertical and horizontal individualism and collectivism, through a questionnaire at the end of the experiment. Each individual was assessed into each of four cultural dimensions: vertical individualism (VI), horizontal individualism (HI), vertical collectivism (VC) and horizontal collectivism (HC) (Singelis et al. 1995). The questionnaire consists of 32 items (on a 7-point scale) which are divided evenly into four dimensions. Maximum likelihood factor analysis was performed with the answers given by the 144 participants. After submitting the results to an oblique rotation, a four-factor solution was obtained. This approach treats the four dimensions as separate, as only loosely correlated dimensions, and allows for personalities characterised by both high (or low) individualism and collectivism at the same time (see Gouveia et al. (2003) for the validity of this approach in a Spanish population). The Cronbach reliabilities for each dimension were: VI = 0.82; HI = 0.75; VC = 0.67; HC = 0.86. These values are in the range shown by previous studies (see Taras et al. 2010;Probst et al. 1999;Oyserman et al. 2002;Gouveia et al. 2003). Table 6 shows a descriptive summary for the whole sample and correlations between the four cultural dimensions, and Fig. 3 displays the distribution of cultural values. Most of the participants in the experiment are classified as high horizontal collectivists, which seems to be a regular pattern in Spain (Hofstede et al. 2010;Gouveia et al. 2003). Furthermore, I find positive and significant correlations between VI and HI ( = 0.31;p < 0.001 ) and between VC and HC ( = 0.32;p < 0.001 ). In contrast, there is a negative and significant correlation between VI and HC ( = −0.21;p = 0.013).
For purposes of this paper, distributional preferences are measured using the vertical and horizontal sub-dimensions. That is, each individual is assessed according to two factors: vertical preferences (VI + VC) and horizontal preferences (HI + HC). The Cronbach reliability is 0.75 for the vertical factor and 0.68 for the horizontal factor. However, I have not included the horizontal preferences in the econometric analysis due to the lack of significance to explain cooperative/competitive behaviour.  Table 7.

General instructions
Welcome.
Thank you for participating in this economic experiment. Depending on your decisions and the decisions of other participants, you can earn a considerable amount of money. How you can earn money is described in these instructions. It is therefore important that you read these instructions carefully.
During the experiment you are not allowed to communicate with any of the other participants in whatever way. If you have any questions, please raise your hand. One of us will go to your table to attend you in private.
Your earnings will be calculated in points. At the end of the experiment, the total points will be converted to euros at the following rate: 20 points = 1 euro You will be paid individually and privately in cash at the end of the experiment. The experiment consists of three phases. You will receive detailed instructions of each phase of the experiment before the start of the respective phase. The following pages describe in detail phase 1 of the experiment.
Instructions for phase 1 In this first phase of the experiment all participants will be randomly divided into groups of three members. Nobody, except the experimenters, knows the composition of the groups. Neither before nor after the experiment will you learn which people are in your group.
At the beginning of the phase, every participant receives an endowment of 20 points. Then, you and the other group members simultaneously decide how to allocate the endowment of 20 points. You have two possibilities: 1. You can allocate points to a group account. 2. You can allocate points to a private account. You have to use your entire endowment. That is, the points you put into the group account and the points you put into the private account have to sum up to 20. You have to make only one decision in this phase: how many points to allocate to the group account. The remaining points will be automatically allocated to the private account. How to calculate your income? Your total income depends on the total number of points in the group account, and the number of points in your private account.
a. Your income from your private account is equal to the number of points you allocated to the private account. For each point you put into the private account you get an income of 1 point. The income of the other group members is not affected by your allocation to your private account. b. Your income from your group account is the sum of the points allocated to the group account by all three members multiplied by 0.5. For each point you put into the group account you and all other group members get an income of 0.5 points. For example, if the sum of points in the group account is 20, then your income from the group account and the income of each group member from the group account is 10. The income from the group account is calculated identically for all group members, i.e., all members of a group receive the same income from the group account regardless of their allocation to the group account.
Your total income in points is therefore: Total income = Income from private account + Income from group account Total income = (Points you allocate to private account) + 0.5×(sum of points allocated by all three members to the group account) You get an income of 1 point for each point you allocate to your private account. If you instead allocate 1 extra point to the group account, your income from the group account increases by 0.5 points ( 1 × 0.5 ) and your income from your private account decreases by 1 point. Note that by doing this the income of other group members increases by 0.5 points. Therefore, the total group income increases by 3 × 0.5 = 1.5 points. Other group members therefore also obtain income if you allocate points to the group account. Note that you also obtain income from points allocated to the group account by other members. You obtain 1 × 0.5 = 0.5 points for each point allocated to the group account by another group member.
It is important to note that all groups are independent of each other, that is, the decisions made by the members of one group do not affect the income of the members of another group and vice versa.
The following examples are for illustrative purposes only: Example 1: Assume that you allocated 0 points to the group account. Suppose that each of your other group members also allocated 0 points to the group account. The total number of points in the group account would be 0. Your income in this phase 1 would be 20 points (= 20 points from your private account and 0 points from the group account). The income of the other members of your group would also be 20 points each.
Example 2: Assume that you allocated 10 points to the group account. Suppose that each of your other group members also allocated 0 points to the group account. The total number of points in the group account would be 10. Your income in this phase 1 would be 15 points (= 10 points from your private account +0.5 × 10 = 5 points from the group account). The income of the other members of your group would be 25 points each (=20 points from their private account +0.5 × 10 = 5 points from the group account).
Example 3: Assume that you allocated 20 points to the group account. Suppose that each of your other group members also allocated 20 points to the group account. The total number of points in the group account would be 60. Your income in this phase 1 would be 30 points (= 0 points from your private account +0.5 × 60 = 30 points from the group account). The income of the other members of your group would also be 30 points each.
Any questions?
Next, we will ask you answer some control questions for your better understanding. Once all participants have correctly answered the control questions, the experiment will start.
Instructions for phase 2 The second phase of the experiment consists of 10 rounds. At the beginning of this phase, all participants will be divided into groups of three members, different from the groups formed in the earlier phase. The composition of the groups will remain the same during the ten rounds. Neither before nor after the experiment will you learn which people are in your group or in any of the other groups.
At the beginning of each round, each member of each group receives an endowment of 20 points. Next, you and the other group members simultaneously decide how many points to allocate to the group account, with the remaining points automatically allocated to the private account as was explained in the earlier phase.
Therefore, in each round, your total income in points is: Total income = Income from private account + Income from group account Total income = (Points you allocate to private account) + 0.5×(sum of points allocated by all three members to the group account) After each round, you will be informed of the total allocation to the group account by your group in the last round, your individual income in the last round and your total accumulated income.
At the beginning of each round will receive an endowment of 20 points. The same procedure will be exactly repeated throughout the ten rounds. The income (in points) you get in every round will be accumulated to determine your total income at the end of the second phase.
Any questions? Instructions for phase 3 The last phase of the experiment also consists of ten rounds. Now, your income will be also influenced by the "rank" that your group has relative to the other groups.
Group composition will stay the same as in phase 2 and will remain constant during the next ten rounds. In other words, the two other members of your group will be the same as before.
The group ranking is based on the total number of points allocated to the group account of your group compared to the other groups.
In the experimental session, there are organisations composed of four groups (groups A, B, C and D). Except for the group rankings, everything remains the same as in phase 2. In each round, each participant receives an endowment of 20 points and has to decide how to allocate them to the group account.
How to calculate your income? In each round, your total income results from multiplying your income (from your private account and from the group account) by a conversion factor.
Total income = [(Points you allocate to private account) + 0.5×(sum of points allocated by all three members to the group account)] × conversion factor Your decision, that is, the number of points you allocate to the group account, influences the total number of points in the group account. The total number of points in the group account determines the rank of your group. The rank determines the conversion factor. The conversion factor influences all your round's income.
The value of the conversion factor is determined by the points allocated to your group account compared to the group account of other groups. Note that all of your income is multiplied by the conversion factor.
For a given contribution, the higher the conversion factor of your group, the higher your income. The group with the highest number of points in the group account is assigned rank 1, which means that this group gets the highest conversion factor of 1.0. The group with the second highest number of points in the group account is assigned rank 2, which means that this group gets a conversion factor of 0.75, and so on. The conversion factor for a given rank is given in the following If more than one group contributes the same number of points to the group account, then they get the same conversion factor. For example if all groups have the same number of points in the group account, they all have the same rank (that is, rank 1) and the same conversion factor (that is, 1.00). If two groups are ranked 1, the group with the third highest number of points in the group account will have the rank 3 and a conversion factor of 0.50 (see table below). Suppose you are a member of group A and suppose you have allocated 10 points to the group account, and the other two members allocated 22 points in total. In this case, the sum of the points in the group account is 32, and the rank of your group is 1. The conversion factor of your group is 1.00. As a consequence your income is: (20 − 10 + 0.5 × 32) × 1.00 = 26 points. Now, suppose you are a member of group D and suppose you have allocated 10 points to the group account. Then, the other two members allocated 0 points in total. In this case, the sum of the points in the group account is 10, and the rank of your group is 4. The conversion factor of your group is 0.25. As a consequence, your income is: (20 − 10 + 0.5 × 10) × 0.25 = 3.75 points.
After each round, you will be informed of the total contribution to all groups, their ranks, the conversion factor of your group and your individual income (last round and accumulated). The income (in points) you get in each round will be accumulated to determine your total income at the end of the third phase.
Any questions? Next, we will ask you answer some control questions for your better understanding. Once all participants have correctly answered the control questions, the third and last phase of the experiment will start. Funding Funding for open access publishing: Universidad de Jaén/CBUA. Financial support from the Spanish Ministry of Education (grant CAS15/00283), Spanish Ministry of Science, Innovation and Universities (research projects RTI2018-097620-B-I00 and PID2021-127736NB-I00) and the Universidad de Jaén (research project EI _ SEJ5 _ 2021) is gratefully acknowledged. The author also acknowledges the helpful suggestions and comments provided by M.P. Espinosa, J. Brandts, A. Chaudhuri, two anonymous referees and the editor Marko Koethenbuerger.

Data availability
The data and material are available from the author upon request.

Code availability
The Stata code used to generate the results is available from the author upon request.

Conflict of interest
The author declares that she has no conflict of interest.
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