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THE DYNAMICS OF THE NASH CORRESPONDENCE ANDn-PLAYER STOCHASTIC GAMES

Author

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  • EILON SOLAN

    (Department of Managerial Economics and Decision Sciences, Kellogg Graduate School of Management, Northwestern University, USA;
    The School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel)

Abstract

Aquitting gameis a sequential game where each player has two actions: tocontinueor toquit, and the game continues as long as no player quits.For every continuation payoffxwe assign a one-shot game, where the payoff if everyone continues isx. We study the dynamics of the correspondence that assigns to every continuation payoff the set of equilibrium payoffs in the corresponding one shot game.The study presented here has an implication on the approach one should take in trying to prove, or disprove, the existence of an equilibrium payoff inn-player stochastic games. It also shows that the minimal length of the period of a periodicδ-equilibrium in three-player quitting games needs not be uniformly bounded forδ>0.

Suggested Citation

  • Eilon Solan, 2001. "THE DYNAMICS OF THE NASH CORRESPONDENCE ANDn-PLAYER STOCHASTIC GAMES," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 291-299.
  • Handle: RePEc:wsi:igtrxx:v:03:y:2001:i:04:n:s0219198901000488
    DOI: 10.1142/S0219198901000488
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    Cited by:

    1. Robert Samuel Simon, 2012. "A Topological Approach to Quitting Games," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 180-195, February.

    More about this item

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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