Abstract
We experimentally investigate the role of information transparency for equilibrium selection in stag hunt coordination games. These games can be transformed from a prisoner’s dilemma game by introducing a centralized reward or punishment scheme. We aim to explore the impact of the disclosure of information on how final payoffs are derived on players’ incentive to coordinate on the payoff-dominant equilibrium. We find that such information disclosure significantly increases the tendency of players to play the payoff-dominant strategy and reduces the occurrence of coordination failure. The mechanism works directly through the positive impact of disclosure on the saliency of the payoff-dominant equilibrium, and indirectly through the positive influence of disclosure on players’ belief about the likelihood of cooperation by the opponent.
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Notes
To be consistent with the literature, we refer to cases where people coordinate on the inefficient equilibrium instead of the Pareto-superior equilibrium as coordination failures.
In their experiment, the coordination games are depicted as a hypothetical setting where a pair of subjects agree to meet up but cannot confirm beforehand their meeting takes place. Two alternative places are given: one is made salient by representing it as a landmark building (e.g., the Chicago Sears Tower) while the other is a small, unknown building (e.g., the AT&T building).
We thank an anonymous referee for pointing this out. For example, assuming that the utility of an inequality averse individual is \(U_i =x_i -\alpha _i \max [{({x_j -x_i });0}]-\beta _i \max [{({x_i -x_j});0}]\) for \(i\ne j, \alpha \ge 0, \hbox { and } \alpha >\beta \). The individual’s degree of envy is captured by \(\alpha \) and the degree of compassion is captured by \(\beta \). It is straightforward to verify that the original prisoner’s dilemma game we used in this paper (see Fig. 1) will be perceived as a coordination game if \(\alpha \ge 0 \hbox { and } \beta >\frac{1}{4}\).
It can be straightforwardly shown that an inequality averse individual with Fehr and Schmidt utility function would still perceive stag hunt games 1 and 2 presented in Fig. 1 as stag hunt games regardless of how averse he (she) is to advantageous or disadvantageous inequality. Indeed, both (C, C) and (D, D) would remain as equilibria for all admissible values of \(\alpha \) and \(\beta \).
Unless stated otherwise, “beliefs” throughout this paper means agents’ beliefs that the other player will cooperate. It measures the subjective probability that the other player would cooperate.
In the instructions, we refer to players as “ROW” or “COLUMN” player. Their strategies “C” and “D” are referred to “Up” and “Down” for the row player, and “Left” and “Right” for the column player. We use “C” and “D” hereafter for convenience.
The instructions used in the experiment can be found in the appendix.
In the punish_stag1 and the reward_stag2 treatments, subjects were presented with both the stag hunt game and the original prisoner’s dilemma game, one might question if subjects understood the game. To prove that subjects did understand the game, we compared the cooperation rate in the prisoner’s dilemma treatment (a treatment where subjects played the original prisoner’s dilemma game) to that in the stag1 and stag2 treatments (the control stag hunt games). It shows that the cooperation rate (C,C) in the prisoner’s dilemma game (see the bar chart for (C,C) in Pd treatment shown in Fig. 5) is much lower than that in the stag hunt games (see the bar charts for (C,C) in Stag1 and Stag2 shown in Fig. 3). This suggests that subject did respond differently to the differing contingencies in these different types of games.
We used subject averages across periods as units of observation, following Charness et al. (2007). Specifically, for each subject we calculated the average cooperation rate over the 25 periods and used it as a unit of observation. That is to say, the number of observations is the number of subjects in each treatment (punish_stag1: \(N= 52\); stag1: \(N = 96\); reward_stag2: \(N = 52\); stag2: \(N = 92\)). It is to eliminate correlation over time. This type of tests throughout the paper follows similar suit unless otherwise stated.
Our study relates to framing in a broad sense as the result is affected by how the game is described. In this strand of literature (e.g., see Erev and Roth 2014 for a review), it has been found that framing seems to come into effect through initial beliefs and therefore the explanatory power of it might be stronger in early periods (Cooper et al. 1990). As a result, the smaller difference between treatments in early periods might be more informative. To verify this, we present the distribution of decision pair types for the first ten periods in figure A3 in supplementary appendix A. Observational conclusions from comparisons between treatments remain the same. We thank an anonymous referee for comments in this regard.
As we used a random matching protocol, the opponent is likely to be different in each of these three periods. The regressor refers to the decision of the opponent in that a particular period.
Since a lagged dependent variable is used as a regressor, we also tried the “difference” and “system” generalized method-of-moments (GMM) dynamic panel estimation method for belief formation in individual treatments (Roodman 2009). However, the long panel T and relatively small N lead to an explosive number of instruments, which may generate bias in estimates as indicated by a perfect Hansen statistic of 1.000.
We also present the results using only the first 10 periods in table A1 in the supplementary appendix A. Conclusions remain qualitatively the same except that the treatment dummy for the reward_stag2 treatment becomes insignificant. It might be because of a smaller difference between the reward_stag2 and stag2 treatments before steady equilibrium is achieved. This result is consistent with the analysis on decision, which suggests that information on these two mechanisms may work differently.
One may worry about the endogeneity of beliefs. On the one hand, it is not uncommon for belief to be used as a regressor in the literature (see, e.g., Charness and Dufwenberg 2006; Croson 2007; Fischbacher and Gächter 2010; Dufwenberg et al. 2011); on the other, we applied the two-stage least squares estimation method, treating belief as an endogenous variable. Our conclusion remains the same.
As for belief formation and cooperation, we also applied the random effects model. Since the estimation results are very similar to OLS, only OLS results are reported.
We present the results using the first ten period in table A2 in the supplementary appendix A. Conclusions remain qualitatively unchanged.
The number of observations in each of treatment is thus equal to the number of subjects participating in each treatment. That is, \(N = 50\) for the pd treatment, \(N = 50\) for the punish_pd treatment, and \(N = 50\) for the reward_pd treatment.
We present the result only using the first ten periods in figure A3 in the supplementary appendix A. Comparisons between the results from the two treatments across all periods show that they are not much different.
References
Balliet, D., Mulder, L. B., & Van Lange, P. A. (2011). Reward, punishment, and cooperation: A meta-analysis. Psychological Bulletin, 137(4), 594.
Bangun, L., Chaudhuri, A., Prak, P., & Zhou, C. (2006). Common and almost common knowledge of credible assignments in a coordination game. Economics Bulletin, 3(1), 1–10.
Battalio, R., Samuelson, L., & Van Huyck, J. (2001). Optimization incentives and coordination failure in laboratory stag hunt games. Econometrica, 69(3), 749–764.
Berninghaus, S. K., & Ehrhart, K.-M. (2001). Coordination and information: Recent experimental evidence. Economics Letters, 73(3), 345–351.
Bohnet, I., & Zeckhauser, R. (2004). Trust, risk and betrayal. Journal of Economic Behavior and Organization, 55(4), 467–484.
Brandts, J., & Cooper, D. J. (2006a). A change would do you good. an experimental study on how to overcome coordination failure in organizations. American Economic Review, 96(3), 669–693.
Brandts, J., & Cooper, D. J. (2006b). Observability and overcoming coordination failure in organizations: An experimental study. Experimental Economics, 9(4), 407–423.
Cason, T.N., Laub, S.H.P., Muic, V.L. (2015). Prior Interaction, Identity, and Cooperation in the Inter-Group Prisoner’s Dilemma. Working paper.
Charness, G., & Dufwenberg, M. (2006). Promises and partnership. Econometrica, 74(6), 1579–1601.
Charness, G., Frechette, G. R., & Qin, C. Z. (2007). Endogenous transfers in the Prisoner’s Dilemma game: An experimental test of cooperation and coordination. Games and Economic Behavior, 60(2), 287–306.
Chaudhuri, A., Schotter, A., & Sopher, B. (2009). Talking ourselves to efficiency: Coordination in inter-generational minimum effort games with private, almost common and common knowledge of advice. Economic Journal, 119(534), 91–122.
Cooper, R., DeJong, D. V., Forsythe, R., & Ross, T. (1990). Selection criteria in coordination games: Some experimental results. American Economic Review, 80(1), 218–233.
Cooper, R., DeJong, D. V., Forsythe, R., & Ross, T. W. (1992). Communication in coordination games. Quarterly Journal of Economics, 107(2), 739–771.
Crawford, V. P., Gneezy, U., & Rottenstreich, Y. (2008). The power of focal points is limited: Even minute payoff asymmetry may yield large coordination failures. American Economic Review, 98(4), 1443–1458.
Croson, R. T. (2007). Theories of commitment, altruism and reciprocity: Evidence from linear public goods games. Economic Inquiry, 45(2), 199–216.
Devetag, G., & Ortmann, A. (2007). When and why? A critical survey on coordination failure in the laboratory. Experimental Economics, 10(3), 331–344.
Dufwenberg, M., Gächter, S., & Hennig-Schmidt, H. (2011). The framing of games and the psychology of play. Games and Economic Behavior, 73(2), 459–478.
Ellingsen, T., Johannesson, M., Mollerstrom, J., & Munkhammar, S. (2012). Social framing effects: Preferences or beliefs? Games and Economic Behavior, 76(1), 117–130.
Erev, I., & Roth, A. E. (2014). Maximization, learning, and economic behavior. Proceedings of the National Academy of Sciences, 111(Supplement 3), 10818–10825.
Fehr, E., & Schmidt, K. M. (1999). A theory of fairness, competition, and cooperation. Quarterly Journal of Economics, 114(3), 817–868.
Fischbacher, U. (2007). z-tree: Zurich toolbox for ready-made economic experiments. Experimental Economics, 10(2), 171–178.
Fischbacher, U., & Gächter, S. (2010). Social preferences, beliefs, and the dynamics of free riding in public goods experiments. American Economic Review, 100(1), 541–556.
Goeree, J. K., Holt, C. A., & Palfrey, T. R. (2003). Risk averse behavior in generalized matching pennies games. Games and Economic Behavior, 45(1), 97–113.
Guala, F., & Mittone, L. (2010). How history and convention create norms: An experimental study. Journal of Economic Psychology, 31(4), 749–756.
Harsanyi, J. C. (1995). A new theory of equilibrium selection for games with complete information. Games and Economic Behavior, 8(1), 91–122.
Harsanyi, J. C., & Selten, R. (1988). A general theory of equilibrium selection in games (Vol. 1). Massachusetts: The MIT Press.
Heinemann, F., Nagel, R., & Ockenfels, P. (2009). Measuring strategic uncertainty in coordination games. The Review of Economic Studies, 76(1), 181–221.
Holt, C. A., & Laury, S. K. (2002). Risk aversion and incentive effects. American Economic Review, 92(5), 1644–1655.
Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263–291.
Rabin, M. (1993). Incorporating fairness into game theory and economics. The American Economic Review, 83(5), 1281–1302.
Roodman, D. (2009). How to do xtabond2: An introduction to difference and system gmm in stata. Stata Journal, 9(1), 86.
Schechter, L. (2007). Traditional trust measurement and the risk confound: An experiment in rural paraguay. Journal of Economic Behavior and Organization, 62(2), 272–292.
Sefton, M., Shupp, R., & Walker, J. M. (2007). The effect of rewards and sanctions in provision of public goods. Economic Inquiry, 45(4), 671–690.
Sigmund, K., Hauert, C., & Nowak, M. A. (2001). Reward and punishment. Proceedings of the National Academy of Sciences, 98(19), 10757–10762.
Skyrms, B. (1996). Evolution of the social contract. Cambridge: cambridge University Press.
Tabellini, G. (2008). The Scope of Cooperation: Values and Incentives. The Quarterly Journal of Economics, 123(3), 905–950.
Teyssier, S. (2012). Inequity and risk aversion in sequential public good games. Public Choice, 151(1–2), 91–119.
Van Huyck, J. B., Battalio, R. C., & Beil, R. O. (1990). Tacit coordination games, strategic uncertainty, and coordination failure. American Economic Review, 80(1), 234–248.
Van Huyck, J. B., Gillette, A. B., & Battalio, R. C. (1992). Credible assignments in coordination games. Games and Economic Behavior, 4(4), 606–626.
Acknowledgments
We thank seminar participants at Annual Conference of the Society for the Advancement of Behavioral Economics (Granada, Spain) for their useful comments. This research benefited from the MOE Tier 1 Grant (RG 79/12 M4011091.00) awarded by Nanyang Technological University to Yohanes E. Riyanto.
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Liu, J., Riyanto, Y.E. Information transparency and equilibrium selection in coordination games: an experimental study. Theory Decis 82, 415–433 (2017). https://doi.org/10.1007/s11238-016-9572-x
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DOI: https://doi.org/10.1007/s11238-016-9572-x