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On Games Of Perfect Information: Equilibria, Ε–Equilibria And Approximation By Simple Games

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  • GUILHERME CARMONA

    (Faculdade de Economia, Universidade Nova de Lisboa, Campus de Campolide, 1099-032 Lisboa, Portugal)

Abstract

We show that every bounded, continuous at infinity game of perfect information has an ε–perfect equilibrium. Our method consists of approximating the payoff function of each player by a sequence of simple functions, and to consider the corresponding sequence of games, each differing from the original game only on the payoff function. In addition, this approach yields a new characterization of perfect equilibria: A strategyfis a perfect equilibrium in such a gameGif and only if it is an1/n–perfect equilibrium inGnfor alln, where{Gn}stands for our approximation sequence.

Suggested Citation

  • Guilherme Carmona, 2005. "On Games Of Perfect Information: Equilibria, Ε–Equilibria And Approximation By Simple Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 491-499.
    • Handle: RePEc:wsi:igtrxx:v:07:y:2005:i:04:n:s0219198905000661
    DOI: 10.1142/S0219198905000661
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    1. Drew Fudenberg & David Levine, 2008. "Limit Games and Limit Equilibria," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 2, pages 21-39, World Scientific Publishing Co. Pte. Ltd..
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    5. Drew Fudenberg & David Levine, 2008. "Subgame–Perfect Equilibria of Finite– and Infinite–Horizon Games," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 1, pages 3-20, World Scientific Publishing Co. Pte. Ltd..
    6. Christopher Harris & John Vickers, 1985. "Perfect Equilibrium in a Model of a Race," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(2), pages 193-209.
    7. Hellwig, Martin & Leininger, Wolfgang & Reny, Philip J. & Robson, Arthur J., 1990. "Subgame perfect equilibrium in continuous games of perfect information: An elementary approach to existence and approximation by discrete games," Journal of Economic Theory, Elsevier, vol. 52(2), pages 406-422, December.
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    Cited by:

    1. János Flesch & Arkadi Predtetchinski, 2016. "Subgame-perfect $$\epsilon $$ ϵ -equilibria in perfect information games with sigma-discrete discontinuities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 479-495, March.
    2. Hannu Salonen & Hannu Vartiainen, 2011. "On the Existence of Markov Perfect Equilibria in Perfect Information Games," Discussion Papers 68, Aboa Centre for Economics.
    3. Francesco Caruso & Maria Carmela Ceparano & Jacqueline Morgan, 2022. "Asymptotic Behavior of Subgame Perfect Nash Equilibria in Stackelberg Games," CSEF Working Papers 661, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    4. János Flesch & Arkadi Predtetchinski, 2017. "A Characterization of Subgame-Perfect Equilibrium Plays in Borel Games of Perfect Information," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1162-1179, November.

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    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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