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Subjective Equilibrium in Repeated Games

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Author Info
Ehud Kalai
Ehud Lehrer

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Abstract

A player's strategy, for an n-person infinitely repeated game with discounting, is subjectively rational if it is a best response to his individual beliefs regarding opponents' strategies. A vector of such strategies is a subjective equilibrium if the play induced by it is realization equivalent to the play induced by each players' beliefs. Thus, any statistical updating can only reinforce the beliefs. It is shown that under perfect monitoring, the joint behavior at a subjective equilibrium approximates a behavior of a Nash equilibrium even when perturbations are allowed. Therefore, learning processes leading to subjective equilibrium result in approximate Nash behavior.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 981.

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Date of creation: Jan 1991
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Handle: RePEc:nwu:cmsems:981

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  1. Michael Peters, 1998. "Limits of Exact Equilibria for Capacity Constrained Sellers with costlySearch," Working Papers peters-98-01, University of Toronto, Department of Economics. [Downloadable!]
    Other versions:
  2. José Penalva & Michael D. Ryall, 2001. "Causal Assessment in Finite Extensive-form Games," Economics Working Papers 483, Department of Economics and Business, Universitat Pompeu Fabra, revised Sep 2003. [Downloadable!]
  3. Alvaro Sandroni, . ""Necessary and Sufficient Conditions for Convergence to Nash Equilibrium: The Almost Absolute Continuity Hypothesis''," CARESS Working Papres 95-08, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences. [Downloadable!]
  4. Matthew O. Jackson & Ehud Kalai, 1997. "False Reputation in a Society of Players," Game Theory and Information 9711004, EconWPA. [Downloadable!]
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  5. Ehud Kalai & Ehud Lehrer, 1992. "Weak and Strong Merging of Opinions," Discussion Papers 983, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  6. Yossi Feinberg & Marco Scarsini, 2003. "Rate of Arbitrage and Reconciled Beliefs," Economics Bulletin, Economics Bulletin, vol. 4(11), pages 1-12. [Downloadable!]
  7. Fehr, Dietmar & Kübler, Dorothea & Danz, David N., 2008. "Information and Beliefs in a Repeated Normal-Form Game," IZA Discussion Papers 3627, Institute for the Study of Labor (IZA). [Downloadable!]
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  8. Shlomit Hon-Snir & Dov Monderer & Aner Sela, 1996. "A Learning Approach to Auctions," Game Theory and Information 9610004, EconWPA, revised 07 Oct 1996. [Downloadable!]
  9. Felipe Pérez, 1998. "- Private Experience In Adaptive Learning Models," Working Papers. Serie AD 1998-03, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
  10. Pierpaolo Battigalli & Marciano Siniscalchi, 2003. "Rationalization and Incomplete Information," Advances in Theoretical Economics, Berkeley Electronic Press, vol. 3(1), pages 1073-1073. [Downloadable!] (restricted)
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  11. Ehud Kalai & Ehud Lehrer, 1990. "Rational Learning Leads to Nash Equilibrium," Discussion Papers 925, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  12. Amegashie, J.A., 2005. "Information Transmission in Elimination Tournaments," Working Papers 2005-11, University of Guelph, Department of Economics. [Downloadable!]
  13. José J. Sempere Monerris & Amparo Urbano & María Dolores Alepuz, 1998. "- Duopoly Price Communication," Working Papers. Serie AD 1998-26, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
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  14. Jimmy Chan, 2000. "On the Non-Existence of Reputation Effects in Two-Person Infinitely-Repeated Games," Economics Working Paper Archive 441, The Johns Hopkins University,Department of Economics.
  15. Alvaro Sandroni, 1997. "Reciprosity and Cooperation in Repeated Coordination Games: The Blurry Belief Approach," Discussion Papers 1200, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  16. Azrieli, Yaron, 2007. "Thinking categorically about others: A conjectural equilibrium approach," MPRA Paper 3843, University Library of Munich, Germany, revised 06 Sep 2007. [Downloadable!]
  17. Mario Gilli, 2002. "Rational Learning in Imperfect Monitoring Games," Working Papers 46, University of Milano-Bicocca, Department of Economics, revised Mar 2002. [Downloadable!]
  18. Felipe Perez, 1997. "Private Experience in Adaptive Learning Models," Levine's Working Paper Archive 1403, UCLA Department of Economics. [Downloadable!]
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  19. Mario Gilli, 1999. "On Non-Nash Equilibria," Levine's Working Paper Archive 2084, UCLA Department of Economics. [Downloadable!]
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  20. Jozsef Sakovics, 2004. "Games of incomplete information without common knowledge priors," ESE Discussion Papers 77, Edinburgh School of Economics, University of Edinburgh. [Downloadable!]
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  21. Patrick Leoni, . "Learning in Repeated Games without Repeating the Game," IEW - Working Papers iewwp215, Institute for Empirical Research in Economics - IEW. [Downloadable!]
  22. Jose Penalva-Zuasti & Michael D. Ryall, 2003. "Causal Assessment in Finite-length Extensive-Form Games," Levine's Working Paper Archive 506439000000000074, UCLA Department of Economics. [Downloadable!]
  23. Roger Lagunoff, 1995. "On the dynamic selection of mechanisms for provisions of public projects," Discussion Paper / Institute for Empirical Macroeconomics 100, Federal Reserve Bank of Minneapolis. [Downloadable!]
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