Abstract
Using a laboratory experiment, we examine whether voluntary sanctions induce subjects to coordinate more efficiently in a repeated minimum-effort game. While most groups first experience Pareto inferior coordination in a baseline treatment, the level of effort increases substantially once ex post sanctioning opportunities are introduced, that is, when one can assign costly punishment points to other group members to reduce their payoffs. We compare the effect of this voluntary punishment possibility with the effect of ex post costless communication, which in contrast to the punishment treatment increases efforts only temporarily and fails to bring the players to higher payoff equilibria permanently. Our results indicate that decentralized sanctions can play an important role as a coordination device in Pareto-ranked coordination settings. They also suggest that the motivations behind voluntary sanctions may be more general than usually put forth in the literature on cooperation games.
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Notes
For instance: Smaller groups Van Huyck et al. (1990); higher incentives in the form of exogenous bonuses Brandts and Cooper (2007) or lower effort costs Goeree and Holt (2005); more refined action space Van Huyck et al. (2007); communication opportunities including pre-play cheap talk (Charness 2000; Clark et al. 2001; Blume and Ortmann 2007; Dugar and Shahriar 2018); ex post disapproval messages Dugar (2010) or centralized communication by a team leader Brandts and Cooper (2007); group composition, either through socio-demographic homogeneity Engelmann and Normann (2010), or endogenous decisions Riedl et al. (2015).
In Bolton and Ockenfels ’ 2000 model, the lowest effort individuals will be targeted more strongly because of the convex inequity disutility.
Another session was run with the baseline condition (32 subjects, 4 groups), but due to a technical problem the second stage of the experiment could not be run. The results of this session are not reported here but are very similar to what is observed in the first stage of the experiment in all treatments.
A probit model with random effects on whether some punishment is exerted or not leads to the same conclusions.
For the Mann–Whitney U test, the statistical power is given by the following parameters: For a standard threshold probability of 0.76 that measure 1 is greater than measure 2, an \(\alpha\) (significance) level at.10 and samples of size 12 correspond to a statistical power of.70.
As a robustness exercise, we checked whether results were affected by the clustering at the subject level, the use of random-effects at the individual level, or changes in specification (ordered logit). None of these changes has a substantial impact on the results and their significance.
The only (weakly) significant test for Stage 1 concerns Baseline/Disapproval for the first round. At worst, it suggests that Disapproval may start slightly higher than the other two treatments (which should invite caution for any positive difference observed in favor of Disapproval), and at best it is a random fluctuation.
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While working on this paper, Rydval was supported by the Czech Science Foundation grant P402/12/G130.
Appendix A: statistical and econometric analyses
Appendix A: statistical and econometric analyses
1.1 Detailed analysis of stage 1 results
The purpose of these additional analyses is to establish the robustness of the findings highlighted in the introduction of sub-section 3.1. In particular, we resort to two main testing strategies. First, we rely on a series of non-parametric two-sided Mann-Whitney U tests to see whether group average efforts and group minimum efforts differ across treatment for subsequent rounds. The detailed results of these tests are provided Table A.2.
Since the number of observations in this (conservative) test is restricted as the unit is the group, we set a significance level at.10.Footnote 5
We complement these tests with an econometric approach relying on an ordered probit on individual efforts regressed with round dummies, treatment dummies and their interactions. The estimations are based on a panel of 256 subjects with 16 rounds of choices each. We use the cluster-robust estimator of variance to take into account intra-group correlation of effort choices. The number of clusters seems sufficient given the perfectly balanced cluster-sizes Kezdi (2004); Rogers (1993).Footnote 6 The detailed results of these estimations are displayed in Table A.1 (column 1). We then test each coefficient associated with interaction terms of the kind Round n \(\times\) Treatment T against 0 with a Wald test: In case of statistical significance, this reads as treatment T has a significant impact at round n in comparison to the Baseline treatment at the same round.
Both these approaches confirm that no effect of treatment can be found in Stage 1 for all rounds: All \(p-\)values are greater than.10 for direct non-parametric comparisons except for one,Footnote 7 and the same applies to the estimated coefficients of our ordered probit. Overall, we find no compelling evidence that subject samples or initial behaviors differ across treatments.
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Lec, F.L., Matthey, A. & Rydval, O. Punishing the weakest link - Voluntary sanctions and efficient coordination in the minimum effort game. Theory Decis 95, 429–456 (2023). https://doi.org/10.1007/s11238-023-09931-1
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DOI: https://doi.org/10.1007/s11238-023-09931-1