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Cooperation in a repeated game with random payment function

Published online by Cambridge University Press:  14 July 2016

Ilan Eshel  and
Daphna Weinshall
Ilan Eshel
Affiliation:
Tel-Aviv University
Daphna Weinshall*
Affiliation:
Tel-Aviv University
*
∗ Postal address: Department of Statistics, School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv, Israel.
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Abstract

A model of cooperation versus defection in a sequence of games is analysed under the assumptions that the rules of the game are randomly changed from one encounter to another, that the decisions are to be made each time anew, according to the (random) rules of the specific local game, and that the result of one such game affects the ability of a player to participate and thus, cooperate in the next game. Under plausible assumptions, it is shown that all Nash solutions of the supergame determine cooperation over a non-degenerate range of rules, determining encounters of the prisoner's dilemma type.

Keywords

STOCHASTIC GAMEESSSUPERGAMECONTINUOUS GAMEPRISONER'S DILEMMA
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 3 , September 1988 , pp. 478 - 491
Copyright
Copyright © Applied Probability Trust 1988 

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Footnotes

Research partly supported by the US-Israel Binational Science Foundation, grant 8500021.

References

Axelrod, R. and Hamilton, W. D. (1981) The evolution of cooperation. Science 211, 1390–1396.Google Scholar
Eshel, I. (1982) Evolutionary stable strategies and viability selection in Mendelian populations. Theoret. Popn. Biol. 22, 204–217.Google Scholar
Eshel, I. (1983) Evolutionary continuous strategies. J. Theoret. Biol. 103, 99–111.Google Scholar
Eshel, I. and Motro, U. (1981) Kin selection and strong evolutionary stability of mutual help. Theoret. Popn. Biol. 19, 420–433.Google Scholar
Eshel, I. and Weinshall, D. (1987) On the evolution of cooperation in encounters of the prisoncer's dilemma type—a stochastic game approach. Amer. Natur.Google Scholar
Kreps, D., Milgrom, P., Roberts, J. and Wilson, R. (1982) Rational cooperation in the finitely-repeated prisoner's dilemma. J. Econom. Theory 27, 245–252.Google Scholar
Megiddo, N. and Widgerson, A. (1986) On play by means of computing machines. Theoretical Aspects of Reasoning About Knowledge, ed. Halpern, J. Y., Morgan Kaufmann Publishers, Los Altos, Ca., 259–274.Google Scholar
Neyman, A. (1985) Bounded complexity justifies cooperation in the finitely repeated prisoner's dilemma. Unpublished.Google Scholar
Radner, R. (1980) Collusive behavior in non-cooperative epsilon-equilibria in oligopolies with long but finite lives. J. Econom. Theory 22, 289–303.Google Scholar
Rapaport, A. (1967) Escape from paradox. Sci. Amer. 217(1), 50–56.Google Scholar
Rubinstein, A. (1986) Finite automata play—the repeated prisoner's dilemma. J. Econom. Theory 39, 83–96.Google Scholar