Instability of defection in the prisoner’s dilemma under best experienced payoff dynamics

Arigapudi, Srinivas and Heller, Yuval and Milchtaich, Igal (2021): Instability of defection in the prisoner’s dilemma under best experienced payoff dynamics. Forthcoming in: Journal of Economic Theory

Abstract

We study population dynamics under which each revising agent tests each strategy k times, with each trial being against a newly drawn opponent, and chooses the strategy whose mean payoff was highest. When k = 1, defection is globally stable in the prisoner’s dilemma. By contrast, when k > 1 we show that there exists a globally stable state in which agents cooperate with probability between 28% and 50%. Next, we characterize stability of strict equilibria in general games. Our results demonstrate that the empirically-plausible case of k > 1 can yield qualitatively different predictions than the case of k = 1 that is commonly studied in the literature.

• Item Type: MPRA Paper
• Language: English
• Keywords: learning, cooperation, best experienced payoff dynamics, sampling equilibrium, evolutionary stability
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games

References

Burton-Chellew, M. N., El Mouden, C., and West, S. A. (2017). Social learning and the demise of costly cooperation in humans. Proceedings of the Royal Society B: Biological Sciences, 284(1853).

Cárdenas, J., Mantilla, C., and Sethi, R. (2015). Stable sampling equilibrium in common pool resource games. games, 6(3):299–317.

Chmura, T. and Güth, W. (2011). The minority of three-game: An experimental and theoretical analysis. Games, 2(3):333–354.

Heller, Y. and Mohlin, E. (2018). Social learning and the shadow of the past. Journal of Economic Theory, 177:426–460.

Johnson, C. R. and Horn, R. A. (1985). Matrix analysis. Cambridge University Press Cambridge.

Kosfeld, M., Droste, E., and Voorneveld, M. (2002). A myopic adjustment process leading to best-reply matching. Games and Economic Behavior, 40(2):270–298.

Kreindler, G. E. and Young, H. P. (2013). Fast convergence in evolutionary equilibrium selection. Games and Economic Behavior, 80:39–67.

Mantilla, C., Sethi, R., and Cárdenas, J. C. (2018). Efficiency and stability of sampling equilibrium in public goods games. Journal of Public Economic Theory.

Mengel, F. (2018). Risk and temptation: A meta-study on prisoner’s dilemma games. The Economic Journal, 128(616):3182–3209.

Mikekisz, J. and Ramsza, M. (2013). Sampling dynamics of a symmetric ultimatum game. Dynamic Games and Applications, 3(3):374–386.

Nax, H. H., Burton-Chellew, M. N., West, S. A., and Young, H. P. (2016). Learning in a black box. Journal of Economic Behavior & Organization, 127:1–15.

Nax, H. H. and Perc, M. (2015). Directional learning and the provisioning of public goods. Scientific reports, 5(1):1–6.

Osborne, M. J. and Rubinstein, A. (1998). Games with procedurally rational players. American Economic Review, pages 834–847.

Oyama, D., Sandholm, W. H., and Tercieux, O. (2015). Sampling best response dynamics and deterministic equilibrium selection. Theoretical Economics, 10(1):243–281.

Ramsza, M. (2005). Stability of pure strategy sampling equilibria. International Journal of Game Theory, 33(4):515–521.

Rowthorn, R. and Sethi, R. (2008). Procedural rationality and equilibrium trust. The Economic Journal, 118(530):889–905.

Salant, Y. and Cherry, J. (2019). Statistical inference in games. Technical report, mimeo.

Sandholm, W. H. (2001). Almost global convergence to p-dominant equilibrium. International Journal of Game Theory, 30(1):107–116.

Sandholm, W. H. (2010). Population games and evolutionary dynamics. MIT press.

Sandholm, W. H., Izquierdo, S. S., and Izquierdo, L. R. (2019). Best experienced payoff dynamics and cooperation in the centipede game. Theoretical Economics,14(4):1347–1385.

Sandholm,W.H.,Izquierdo,S.S.,andIzquierdo,L.R.(2020). Stability for best experienced payoff dynamics. Journal of Economic Theory, 185.

Sethi, R. (2000). Stability of equilibria in games with procedurally rational players. Games and Economic Behavior, 32(1):85–104.

Sethi, R. (2019). Procedural rationality in repeated games. Unpublished manuscript, Barnard College, Columbia University.

Spiegler, R. (2006a). Competition over agents with boundedly rational expectations. Theoretical Economics, 1(2):207–231.

Spiegler,R.(2006b). The market for quacks. The Review of Economic Studies,73(4):1113–1131.