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The strenght of a little perfection

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Abstract

The paper deals with three related issues.

  1. 1.

    It introduces a measure of partial subgame perfection for equilibria of repeated games.

  2. 2.

    It illustrates that the folk-theorem discontinuity generated by small complexity costs, as exhibited by Abreu and Rubinstein, does not exist in the presence of any level of perfection.

  3. 3.

    It shows that reactive strategy equilibria, such as tit-for-tat, cannot be subgame perfect, even partially so. As a corollary, this shows a need to use full automata rather than exact automata when studying complexity and perfection in repeated games.

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References

  • Abreu D (1988) On the Theory of Infinitely Repeated Games with Discounting, Econometrica, 56 (2), 383–396.

    Google Scholar 

  • Abreu D, Rubinstein A (1988) The Structure of Nash Equilibrium in Repeated Games with Finite Automata, Econometrica, 56 (6), 1259–1281.

    Google Scholar 

  • Aumann RJ, Shapley LS (1976) Long Term Competition: A Game Theoretic Analysis, mimeo, Hebrew University.

    Google Scholar 

  • Aumann RJ (1981) Survey of Repeated Games, in Essays in Game Theory and Mathematical Economics in Honor of Oskar Morgenstern, Wissenschaftsverlag, Bibliographisches Institut, Mannheim, Wien, Zürich 11–42.

    Google Scholar 

  • Aumann RJ (1988) Irrationality in Game Theory, presented at the International Conference on Economic Theories of Politics, Haifa.

  • Ben-Porath E (1986) Repeated Games with Finite Automata, manuscript, Hebrew University.

  • Ben-Porath E, Peleg A (1987) On the Folk Theorem and Finite Automata, manuscript, Hebrew University.

  • Binmore K (1987) Modeling Rational Players I, Economics and Philosophy, 3, 179–214.

    Google Scholar 

  • Fudenberg D, Maskin E (1986) The Folk Theorem in Repeated Games with Discounting or With Incomplete Information, Econometrica, 53 (3), 533–554.

    Google Scholar 

  • Fudenberg D, Maskin E (1987), Nash and Perfect Equilibria of Discounted Repeated Games, Discussion Paper No. 1301, Harvard University.

  • Harsanyi JC, Selten R (1988) A General Theory of Equilibrium Selection in Games, The MIT press, Cambridge.

    Google Scholar 

  • Kalai E, Samet D, Stanford W (1988) A Note on Reactive Equilibria in the Discounted Prisoners' Dilemma and Associated Games, International Journal of Game Theory, 18 (3), 177–186.

    Google Scholar 

  • Kalai E, Stanford W (1988) Finite Rationality and Interpersonal Complexity in Repeated Games, Econometrica, 56 (2), 397–410.

    Google Scholar 

  • Kalai E (1990) Bounded Rationality and Strategic Complexity in Repeated Games, in Game Theory and Applications, Ichiishi, Neyman and Tauman (eds.), Academic Press, San Diego, 131–157.

    Google Scholar 

  • Kohlberg E, Mertens JF (1986) On the Strategic Stability of Equilibria, Econometrica, 54, 1003–1037.

    Google Scholar 

  • Kreps D, Wilson R (1982) Sequential Equilibria, Econometrica, 50, 863–894.

    Google Scholar 

  • Marschak T, Selten R (1978) Restabilizing Resources, Inertia Supergames, and Oligopolistic Equilibria, Quarterly Journal of Economics, 42, 71–93.

    Google Scholar 

  • Neme A, Quintas L (1988) Equilibrium of Repeated Games with Cost of Implementation, Discussion Paper No. 763, Northwestern University.

  • Neyman A (1985) Bounded Complexity Justifies Cooperation in the Finitely Repeated Prisoners' Dilemma, Economic Letters, 19, 227–229.

    Google Scholar 

  • Rosenthal R (1981) Games of Perfect Information, Predatory Pricing and the Chain-Store Paradox, Journal of Economic Theory, 25, 92–100.

    Google Scholar 

  • Rubinstein A (1979) Equilibrium in Supergames with the Overtaking Criterion, Journal of Economic Theory, 21, 1–9.

    Google Scholar 

  • Rubinstein A (1986) Finite Automata Play the Repeated Prisoner's Dilemma, Journal of Economic Theory, 39, 83–96.

    Google Scholar 

  • Selten R (1975) Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games, International Journal of Game Theory, 4, 25–55.

    Google Scholar 

  • Selten R (1978) The Chain Store Paradox, Theory and Decisions, 9, 127–159.

    Google Scholar 

  • Sorin S (1988) Repeated Garnes with Bounded Rationality, forthcoming in Models of Incomplete Information and Bounded Rationality, Proceedings of NATO-ASI, Anacapri.

  • Stanford W (1986) Subgame Perfect Reaction Function Equilibria in Discounted Duopoly Supergames are Trivial, Journal of Economic Theory, 39, 226–232.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Managerial Economics and Decision Sciences, J. L. Kellogg Graduate School of Management, Northwestern University, 2001 Sheridan Road, 60208, Evanston, Illinois

    E. Kalai

  2. IMASL, Universidad Nacional de San Luis, Chacabuco y Pedernera, 5700, San Luis, Argentina

    A. Neme

Authors
  1. E. Kalai
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  2. A. Neme
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Additional information

This work was done while this author was visiting at the Department of Managerial Economics and Decision Sciences, J. L. Kellogg Graduate School of Management, Northwestern University.

Kalai's research is partially supported by National Science Foundation Economics Grants No. SES-8720342 and SES-9011790.

The authors wish to thank Ehud Lehrer, Roger Myerson, Ariel Rubinstein, Nancy Stokey, and anonymous referees of this journal for helpful comments and discussions.

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Kalai, E., Neme, A. The strenght of a little perfection. Int J Game Theory 20, 335–355 (1992). https://doi.org/10.1007/BF01271130

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  • DOI: https://doi.org/10.1007/BF01271130

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