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Testing threats in repeated games

  • Spiegler, Ran

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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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 121 (2005)
Issue (Month): 2 (April)
Pages: 214-235

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Handle: RePEc:eee:jetheo:v:121:y:2005:i:2:p:214-235
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Spiegler, R., 1999. "Reason-Based Choice and Justifiability in Extensive Form Games," Papers 19-99, Tel Aviv.
  2. Reinhard Selten & Michael Mitzkewitz & Gerald R. Uhlich, 1997. "Duopoly Strategies Programmed by Experienced Players," Econometrica, Econometric Society, vol. 65(3), pages 517-556, May.
  3. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
  4. Rubinstein, Ariel, 1986. "Finite automata play the repeated prisoner's dilemma," Journal of Economic Theory, Elsevier, vol. 39(1), pages 83-96, June.
  5. Philippe Jeniel, 2001. "Analogy-Based Expectation Equilibrium," Economics Working Papers 0003, Institute for Advanced Study, School of Social Science.
  6. 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).
  7. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, June.
  8. Spiegler, Ran, 2002. "Equilibrium in Justifiable Strategies: A Model of Reason-Based Choice in Extensive-Form Games," Review of Economic Studies, Wiley Blackwell, vol. 69(3), pages 691-706, July.
  9. 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.
  10. Eliaz, K., 2001. "Nash Equilibrium When Players Account for the Complexity of their Forecasts," Papers 2001-6, Tel Aviv.
  11. 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.
  12. Rubinstein, Ariel, 1991. "Comments on the Interpretation of Game Theory," Econometrica, Econometric Society, vol. 59(4), pages 909-24, July.
  13. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
  14. 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.
  15. Osborne, Martin J & Rubinstein, Ariel, 1998. "Games with Procedurally Rational Players," American Economic Review, American Economic Association, vol. 88(4), pages 834-47, September.
  16. 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.
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