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Testing Threats in Repeated Games

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  • Ran Spiegler

Abstract

I introduce a solution concept for infinite-horizon games, called “Nash equilibrium with added tests”, in which players optimize with respect to relevant threats only after having tested them before. Both the optimal response and the tests are part of equilibrium behavior. The concept is applied to repeated 2×2 games and yields the following results: 1) Sustained cooperation in games such as the Prisoner’s Dilemma is preceded by a “build up” phase, whose comparative statics are characterized. 2) Sustainability of long-run cooperation by means of familiar selfenforcement conventions varies with the payoff structure. E.g., “constructive reciprocity” achieves cooperation with minimal buildup time in the Prisoner’s Dilemma, yet it is inconsistent with long-run cooperation in Chicken. 3) Nevertheless, a “folk theorem” holds for this class of games.
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  • Ran Spiegler, 2002. "Testing Threats in Repeated Games," NajEcon Working Paper Reviews 391749000000000445, www.najecon.org.
  • Handle: RePEc:cla:najeco:391749000000000445
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    1. Reinhard Selten & Michael Mitzkewitz & Gerald R. Uhlich, 1997. "Duopoly Strategies Programmed by Experienced Players," Econometrica, Econometric Society, vol. 65(3), pages 517-556, May.
    2. Kreps, David M. & Milgrom, Paul & Roberts, John & Wilson, Robert, 1982. "Rational cooperation in the finitely repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 27(2), pages 245-252, August.
    3. Spiegler, R., 1999. "Reason-Based Choice and Justifiability in Extensive Form Games," Papers 19-99, Tel Aviv.
    4. Rubinstein, Ariel, 1991. "Comments on the Interpretation of Game Theory," Econometrica, Econometric Society, vol. 59(4), pages 909-924, July.
    5. Reinhard Selten & Michael Mitzkewitz & Gerald R. Uhlich, 1997. "Duopoly Strategies Programmed by Experienced Players," Econometrica, Econometric Society, vol. 65(3), pages 517-556, May.
    6. Spiegel, Mark M., 1995. "Threshold effects in international lending," Journal of Development Economics, Elsevier, vol. 46(2), pages 341-356, April.
    7. Osborne, Martin J & Rubinstein, Ariel, 1998. "Games with Procedurally Rational Players," American Economic Review, American Economic Association, pages 834-847.
    8. Jehiel, Philippe, 2005. "Analogy-based expectation equilibrium," Journal of Economic Theory, Elsevier, pages 81-104.
    9. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
    10. Ehud Kalai & William Stanford, 1986. "Finite Rationality and Interpersonal Complexity in Repeated Games," Discussion Papers 679, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    11. Banks, Jeffrey S. & Sundaram, Rangarajan K., 1990. "Repeated games, finite automata, and complexity," Games and Economic Behavior, Elsevier, vol. 2(2), pages 97-117, June.
    12. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, pages 1019-1045.
    13. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, pages 1-18.
    14. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, pages 6-38.
    15. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, January.
    16. Eliaz, Kfir, 2003. "Nash equilibrium when players account for the complexity of their forecasts," Games and Economic Behavior, Elsevier, vol. 44(2), pages 286-310, August.
    17. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-1281, November.
    18. Rubinstein, Ariel, 1986. "Finite automata play the repeated prisoner's dilemma," Journal of Economic Theory, Elsevier, pages 83-96.
    19. Kalai, Ehud & Stanford, William, 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, Econometric Society, vol. 56(2), pages 397-410, March.
    20. Ran Spiegler, 2002. "Equilibrium in Justifiable Strategies: A Model of Reason-based Choice in Extensive-form Games," Review of Economic Studies, Oxford University Press, vol. 69(3), pages 691-706.
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    Cited by:

    1. Hubie Chen, 2013. "Bounded rationality, strategy simplification, and equilibrium," International Journal of Game Theory, Springer;Game Theory Society, pages 593-611.
    2. Ran Spiegler, 2006. "The Market for Quacks," Review of Economic Studies, Oxford University Press, vol. 73(4), pages 1113-1131.

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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