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Splitting leagues: promotion and demotion in contribution-based regrouping experiments

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Abstract

The paper reports an experimental study on a promotion-demotion mechanism to mitigate the free-rider problem in a voluntary contribution setting. The mechanism hierarchically splits a group in two; we refer to one subgroup as the Major league and to the other as the minor league. The most cooperative subject of the minor league is switched with the least cooperative subject in the Major league. The results reveal a significant increase of cooperation levels in both leagues relative to the standard voluntary contribution mechanism. We argue that a lack of sequentially-rational beliefs about continuation payoffs in Major and minor leagues leads to higher equilibrium contributions. The data suggest beyond that, the promotion-demotion mechanism regroups subjects deliberately according to their cooperativeness.

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Notes

  1. Some studies have investigated the use of promotions and demotions to provide incentives in work or sports environments (e.g., Lazear 1992; Kräkel 2006; and Belzil and Bognanno 2008).

  2. In Page et al. (2005), reputation-building creates the rationale for beliefs in a positive continuation-payoff.

  3. Two stylized facts are that subjects contribute between 40 % and 60 % of their endowment to the group project in the first round of the finitely repeated game and that contributions decline in the sequel (surveys are provided in Hey 1991; Davis and Holt 1993; Ledyard 1995; and Keser 2002).

  4. This initial group-assignment rule was common information to participants.

  5. The differential is bounded between 0≤(α Mi −α mi )≤75 since the continuation payoffs depend on the others’ contributions. At best, for the player in the Major league, the others contribute everything and, at worst, for the player in the minor league, the others contribute nothing. Thus, the advantage of being in the Major league in the next round can not exceed 75. On the other hand, if players do not care about their future location the expected advantage of being in the Major league is zero.

  6. An asymmetric contribution profile cannot be part of a perfect Bayesian-Nash equilibrium since some players can always do better by lowering their contributions.

  7. Note that the line of reasoning is the same for mixed strategies as the increment in the probability corresponds to a higher probability of being promoted and a higher expected payoff.

  8. There is more experimental evidence of heterogeneous, non-sequentially-rational beliefs; e.g., see the literature on the beauty-contest experiment (Nagel 1995).

  9. It is noteworthy that this example allows time-consistent beliefs in the repeated setting since the two players who hold wrong beliefs about the Major league have no opportunity to update them given that they are affiliated to the minor league always.

  10. We theoretically discuss the impact of sequential rationality of strictly self-interested players in this paper only. A more general behavioral model would have to take account of the fact that people are heterogeneous with regards to their homegrown willingness-to-cooperate and their beliefs about others.

  11. Note that players are assumed to anticipate the others’ contributions as they form their expectations about the continuation payoff at a time, when they have not observed the others’ contributions. The assumption that experimental subjects actually form their expectations based on these anticipated contributions is, admittedly, quite demanding. Yet, it seems less demanding than alternative assumptions as, for instance, perfect foresight. Under the perfect-foresight assumption, one arguably biased estimate of the continuation-payoff differential between the leagues would be the difference of the average contributions in the two leagues during the last nine rounds (see Table 1) which is 34 Eurocents.

  12. We reach at a very similar estimation, i.e., \(\hat{\alpha}_{M} = 62\) \([\hat{\alpha}_{M} = 32 ]\), if we neglect the assumed expectations of the subjects who are moving from one league to the other.

  13. The p-value of the two-tailed Wilcoxon signed ranks test is 0.767.

  14. Compared to the VCM treatment, the payoffs in the Leagues treatment were significantly greater. Only two of the eighty participants in the Leagues treatment ended up earning less than the average round-payoff of 0.66 € the most cooperative group in the VCM achieved. Similarly, only seven subjects of the eighty participants in the Leagues treatment contributed less than the average contribution in the VCM which was 32 % of the endowment (as in the scaling of Fig. 1).

  15. With reference to the behavior of demoted and promoted subjects, we observe that 61 % of the demoted subjects increased their contributions and 63 % of the promoted subjects decreased their contributions in the following round, and 23 % and 24 % did not change their contribution, respectively.

  16. For instance, if all four players in the Major league contribute all their endowment and those in the minor league contributed nothing, one of the high contributors will be demoted and one of the defectors will be promoted.

  17. A similar approach was used in Neugebauer et al. (2009). In particular, we use here the one-step least squares approach which employs the lagged variables as instruments (Arellano and Bond 1991). The p-values of the Sargan test of over-identifying restrictions and the m1 and m2 statistics are 0.000, 0.000 and 0.516, respectively. Thus the validity of the instruments and the absence of misspecified dynamic structures are verified.

  18. Initial contributions are not significantly different to those of the VCM (one-tailed Mann-Whitney test, p=0.183).

  19. The non-declining pattern of contributions in the Random-Position treatment reflects the fact that the more cooperative subjects move to the Major league also in the two control treatments.

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Authors and Affiliations

  1. University of Málaga, Málaga, Spain

    Susana Cabrera

  2. University of East Anglia, Norwich, UK

    Enrique Fatás

  3. GLOBE, University of Granada, Granada, Spain

    Juan A. Lacomba

  4. LSF, University of Luxembourg, Luxembourg, Luxembourg

    Tibor Neugebauer

Authors
  1. Susana Cabrera
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  2. Enrique Fatás
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  3. Juan A. Lacomba
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  4. Tibor Neugebauer
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Corresponding author

Correspondence to Juan A. Lacomba.

Additional information

We thank Jacob Goeree, two anonymous referees and seminar participants at Tucson and Magdeburg for helpful comments. Financial support from the Spanish Ministry of Education and Science (ECO2010-20584), Generalitat Valenciana (PROMETEO/2009/068) and Junta de Andalucíia (P07-SEJ-3261) is gratefully acknowledged. An earlier title of the paper has been “Vertically Splitting a Firm: Promotion and Relegation in a Team Production Experiment”.

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Cabrera, S., Fatás, E., Lacomba, J.A. et al. Splitting leagues: promotion and demotion in contribution-based regrouping experiments. Exp Econ 16, 426–441 (2013). https://doi.org/10.1007/s10683-012-9346-4

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