Evolution towards efficient coordination in repeated games, preliminary version

Demichelis, Stefano (2012): Evolution towards efficient coordination in repeated games, preliminary version.

Abstract

We show that in long repeated games- or in infinitely repeated games with discount rate close to one- payoffs corresponding to evolutionary stable sets are asymptotically efficient, as intuition suggests. Actions played at the beginning of the game are used as messages that allow players to coordinate on Pareto optimal outcomes in the following stages. Strategies following some simple and intuitive "behavioral maxims" are shown to be able to drive out inefficient ones from a population. The result builds a bridge between the theory of repeated games and that of communication games that will be further investigated.

• Item Type: MPRA Paper
• Language: English
• Keywords: Repeated Games, Evolution, Communication, Efficiency
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory

References

R. Aumann, Nash equilibria are not self enforcing, IJGT.

J.P. Benoit, V. Krishna, Finitely Repeated Games, Econometrica, Vol. 53, No. 4 (Jul., 1985), pp. 905-922.

K G. Binmore, L. Samuelson, Evolutionary Stability in Repeated Games Played by Finite Automata, JET 57, 278-305,(1992).

Cima A., F. Ma˜nosas and J. Villadelprat, A Poincar´e-Hopf theoremfor noncompact manifolds, Topology, 37 (1998), 261-277.

S. Demichelis, On several Misconceptions on Evolution and Rationality in Game Theory, in preparation.

S. Demichelis, Efficient Communication and Repetition: an Evolutionary Foundation of Conversational Maxims, in preparation.

S.Demichelis and K.Ritzberger, From evolutionary to strategic stability, Journal of Economic Theory, (2003).

S.Demichelis, K. Ritzberger, and J.Swinkels, The SimpleGeometry of Perfect Information Games, IHS WorkingPaper 115, (2002), International Journal of Game Theory.

S. Demichelis, J. Weibull, ”Language, Meaning, and Games: A Model of Communication, Coordination, and Evolution,” American Economic Review, vol. 98(4), pages 1292-1311, September.

Dreber A, DG Rand, D Fudenberg, MA Nowak (2008). Winners don’t punish. Nature 452: 348-351

R. Durrett: Brownian motion and martingales in analysis,Wadsworth Pub. Co.

D. Fudenberg, E. Maskin (1990):”Evolution and Cooperation in Noisy Repeated Games”, American Economic Review, 80, 274-279.

D. Fudenberg, E. Maskin (2007):”Evolution and Repeated Games”, preprint.

P. Grice, ”Logic and conversation”. In Cole, P. and Morgan, J. (eds.) Syntax and semantics, vol 3. New York: Academic Press,1975.

I.Karatzas, S. Shreve ,Browniam motion and Stochastic calculus,Springer.

Y. Kim and J.Sobel, An Evolutionary Approach to Pre-Play Communication, Econometrica, Vol. 63, No. 5 (Sep., 1995), pp. 1181-1193.

S. Levinson, Pragmatics, Cambridge University Texts, 1983.

G. J. Mailath, L. Samuelson, Repeated Games and Reputations, Oxford, (2006).

J. Maynard Smith, Price, G.R. (1973). ”The logic of animal conflict”. Nature 246 (5427): 1518.

B. Thomas (1985):On evolutionarily stable sets, J. Math. Biology 22, 105-115.

D. Revuz, M.Yor, Continuous Martingales and Brownian Motion,Springer