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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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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 391749000000000445.

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Date of creation: 13 Jan 2002
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Handle: RePEc:cla:levarc:391749000000000445

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  1. Eliaz, K., 2001. "Nash Equilibrium When Players Account for the Complexity of their Forecasts," Papers 2001-6, Tel Aviv.
  2. Ariel Rubinstein, 1997. "Finite automata play the repeated prisioners dilemma," Levine's Working Paper Archive 1639, David K. Levine.
  3. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
  4. Martin J. Osborne & Ariel Rubinstein, 1997. "Games with Procedurally Rational Players," Department of Economics Working Papers 1997-02, McMaster University.
  5. Philippe Jeniel, 2001. "Analogy-Based Expectation Equilibrium," Economics Working Papers 0003, Institute for Advanced Study, School of Social Science.
  6. Kalai, Ehud & Stanford, William, 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, Econometric Society, vol. 56(2), pages 397-410, March.
  7. Banks, J.S. & Sundaram, R.K., 1989. "Repeated Games, Finite Automata, And Complexity," RCER Working Papers 183, University of Rochester - Center for Economic Research (RCER).
  8. Selten,Reinhard & Mitzkewitz,Michael & Uhlich,Gerald, . "Duopoly strategies programmed by experienced players," Discussion Paper Serie B 106, University of Bonn, Germany.
  9. Rubinstein, Ariel, 1991. "Comments on the Interpretation of Game Theory," Econometrica, Econometric Society, vol. 59(4), pages 909-24, July.
  10. David Kreps & Paul Milgrom & John Roberts & Bob Wilson, 2010. "Rational Cooperation in the Finitely Repeated Prisoners' Dilemma," Levine's Working Paper Archive 239, David K. Levine.
  11. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
  12. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-81, November.
  13. 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.
  14. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
  15. Spiegler, R., 1999. "Reason-Based Choice and Justifiability in Extensive Form Games," Papers 19-99, Tel Aviv.
  16. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
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Cited by:
  1. Rani Spiegler, 2005. "The Market for Quacks," Levine's Bibliography 784828000000000634, UCLA Department of Economics.
  2. Hubie Chen, 2013. "Bounded rationality, strategy simplification, and equilibrium," International Journal of Game Theory, Springer, vol. 42(3), pages 593-611, August.

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