Abstract
The aim of this paper is to study the role of the “common reason to believe” (Sugden in Philos Explor 16:165–181, 2003) and the reduction of social distance within the theory of team reasoning. The analysis draws on data collected through a Traveler’s Dilemma experiment. To study the role of the common reason to believe, players’ beliefs in their counterparts’ choices are elicited, and the correlation between the endorsement of team reasoning and beliefs is considered. The relation between social distance and team reasoning is analyzed by introducing a meeting between the two players after the game. We show that the common reason to believe appropriately explains the internal logic of team reasoning and that a reduction of social distance does not produce any statistically significant effect on the probability that team reasoning will be used.
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Notes
We cannot exclude that other reasons, such as the fear of being sanctioned by the counterpart, other than the adoption of team reasoning, may explain the emergence of this subjects’ behavior when a meeting after the game is introduced. We discuss this possibility in Sect. 5.
A footnote specifies that “team reasoning, narrowly defined” means “a mode of reasoning, followed by one individual, which prescribes that he should perform his part of whichever profile is best for the team” (Sugden 2003, p. 168).
The external problem concerns the question: “Should I endorse this mode of reasoning?” That is, even if I am sure that other members of the group will use team reasoning, should I do the same?
This hypothesis is compatible with Ellingsen et al. (2012) interpretation of team reasoning “as an internalized social norm that requires players to unconditionally pick the strategy profile that is consistent with joint payoff maximization” (p. 120). The reference is to Bacharach’s idea of unconditional adoption of team reasoning but, as the authors acknowledge, can be easily extended to Sudgen’s hypothesis of the conditional nature of team reasoning.
The instructions for the experiment are available from the authors upon request.
We believe that in this context, a prize given exclusively for a correct guess might be considered to be too difficult to win, thereby increasing the likelihood of casual answers. At the same time, procedures to elicit beliefs based on quadratic scoring rules (Davis and Holt 1993) are useless for a game—like our version of the Traveler’s Dilemma—which is characterized by a wide range of possible strategies. The use of tolerance thresholds for subjects’ guesses is used in the literature as a valid method for elicitation of beliefs (see, for example, Charness and Dufwenberg 2006; Croson 2000).
Subjects were recruited by e-mail from students on the mailing list of the two laboratories. Fourteen days before the experiment, they received an e-mail with an invitation to visit the Laboratory website for information about the experiment and subscriptions.
An individually self-interested player with a belief different from \( \underline{B} \) would maximize his/her payoff by choosing C i = B i(j) − 1. However, the decision to choose C i < B i(j) − 1 also reveals a clear intention to obtain the reward by undercutting the counterpart’s choice. Indeed, we classify all subjects who choose C i < B i(j) as individually self-interested players. This also takes into account that almost all the players in our experiment (and in the Traveler’s Dilemma game in general, according to the existing literature: Sect. 3.1) did not behave in the way standard game theory would predict that perfectly rational players would behave (choosing \( \underline{C} \) with a belief equal to \( \underline{B} \)).
Even though we find a high percentage of subjects who would be ready to pay the penalty (subjects who choose a number higher than their belief, see p. 19), this behavior is not adopted by subjects who implement team reasoning. Because of this, we can be confident that the C i > B i(j) behavior is not salient for these subjects or that it is less salient than the idea of team reasoning that they are actually implementing.
In the Traveler’s Dilemma, a player who endorses team reasoning and has a belief B i(j) ≠ \( \overline{B} \) will maximize the joint outcome by choosing C i = B i(j) ≠ \( \overline{B} \).
We also investigated the correlation between personal characteristics like age, gender, and income and the likelihood of the emergence of team reasoning, but we did not find any significant effect.
We focus on the VET treatment for a specific reason. Studies on relational goods highlight that even though relational goods may be created through encounters that take place in different environments, some circumstances seem more suitable than others. In particular, relations which are not constrained but which people voluntarily decide to commence are more effective for generating relational goods. For this reason, we may assume (as Becchetti et al. 2010 do) that players in the CET may think that the “forced” encounter after the game is not a good occasion for producing relational goods. Experimental results confirm this interpretation (see Becchetti et al. 2010).
According to our previous definitions, an individually self-oriented player chooses at least one unit below his/her “true” belief regarding his/her counterpart’s choice (C i < B i(j)), while a team reasoning player chooses a number equal to his/her “true” belief. In both these cases, players may decide to declare a belief lower than their choice so as to hedge against two possible risks. First, the risk that their counterpart undercuts their choice (in this case they would incur in the penalty). Second, but only with respect to the self-interested players, the risk that the counterpart chooses exactly the same number as they do, in this way not allowing them to obtain the prize. In the first case (undercutting situation) an hedging strategy (the more effective in case the player reasonable relies on his/her “true” belief) is to declare B i(j) = C i − 11. In the second case, an effective hedging strategy could be to declare a B i(j) = C i − 10. Our data reveal that no players follow the B i(j) = C i − 11 hedging strategy, while the behavior of 16 players (25.00 % of players who choose C i > B i(j)) is compatible with the B i(j) = C i − 10 strategy. We may not exclude that other strategies which result in a decision C i > B i(j) are motivated by less intuitive hedging strategy.
We would like to thank an anonymous referee for his/her suggestion regarding this possible interpretation.
This difference (30.00 % against 27.50 %) is less evident where strategic beliefs are considered.
Note that we do not find an effect of the different treatments on the number of subjects who behave like individually self-interested players (Table 4, columns 4 and 5): the effect of the compulsory meeting on the number of team reasoning players is mainly due to the reduction in the number of players who choose a number higher than their belief. In fact, the percentage of this kind of players is significantly lower in the compulsory meeting treatment (42.50 %) compared to the baseline (50.00 %).
Note that in performing these tests we compare only two treatments, the CET and the baseline. This significantly reduces our sample. We are not totally confident that the results would not change if there were a larger sample.
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Appendices
Appendix 1: Timing of the experiment
Appendix 2
Figures 1, 2, and 3 show the relation between choice and belief across the different treatments. If we compare the single choice options, we note a concentration around the maximum choice (chosen by 11 people in the baseline, 12 people in the CET, and 12 in the VET). However, the wide majority of players pick a number higher than the Nash equilibrium solution (20) and lower than 200, with different combinations of choice and belief, with the majority of players choosing C i > B i(j) (around 45.00 %) and C i < B i(j) (around 37.00 %).
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Becchetti, L., Degli Antoni, G. & Faillo, M. Team reasoning theory: an experimental analysis of common reason to believe and social distance. Int Rev Econ 60, 269–291 (2013). https://doi.org/10.1007/s12232-013-0182-4
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DOI: https://doi.org/10.1007/s12232-013-0182-4