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Characterizing existence of equilibrium for large extensive form games: a necessity result

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  • Carlos Alós-Ferrer

    (University of Cologne)

  • Klaus Ritzberger

    (Vienna Graduate School of Finance and Institute for Advanced Studies)

Abstract

What is the minimal structure that is needed to perform equilibrium analysis in large extensive form games? To answer this question, this paper provides conditions that are simultaneously necessary and sufficient for the existence of a subgame perfect equilibrium in any well-behaved perfect information game defined on a large game tree. In particular, the set of plays needs to be endowed with a topology satisfying two conditions. (a) Nodes are closed as sets of plays; and (b) the immediate predecessor function is an open map.

Suggested Citation

  • Carlos Alós-Ferrer & Klaus Ritzberger, 2017. "Characterizing existence of equilibrium for large extensive form games: a necessity result," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 407-430, February.
    • Handle: RePEc:spr:joecth:v:63:y:2017:i:2:d:10.1007_s00199-015-0937-0
    DOI: 10.1007/s00199-015-0937-0
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    References listed on IDEAS

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    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Solan, Eilon & Vieille, Nicolas, 2003. "Deterministic multi-player Dynkin games," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 911-929, November.
    3. Carlos Alós-Ferrer & Klaus Ritzberger, 2013. "Large extensive form games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 75-102, January.
    4. János Flesch & Jeroen Kuipers & Ayala Mashiah-Yaakovi & Gijs Schoenmakers & Eilon Solan & Koos Vrieze, 2010. "Perfect-Information Games with Lower-Semicontinuous Payoffs," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 742-755, November.
    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. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    7. Carlos Alós-Ferrer & Klaus Ritzberger, 2005. "Trees and decisions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(4), pages 763-798, June.
    8. Harris, Christopher J, 1985. "Existence and Characterization of Perfect Equilibrium in Games of Perfect Information," Econometrica, Econometric Society, vol. 53(3), pages 613-628, May.
    9. Harris, Christopher, 1985. "A characterisation of the perfect equilibria of infinite horizon games," Journal of Economic Theory, Elsevier, vol. 37(1), pages 99-125, October.
    10. Erzo G. J. Luttmer & Thomas Mariotti, 2003. "The Existence of Subgame-Perfect Equilibrium in Continuous Games with Almost Perfect Information: A Comment," Econometrica, Econometric Society, vol. 71(6), pages 1909-1911, November.
    11. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2008. "Trees and extensive forms," Journal of Economic Theory, Elsevier, vol. 143(1), pages 216-250, November.
    12. Roger A. Purves & William D. Sudderth, 2011. "Perfect Information Games with Upper Semicontinuous Payoffs," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 468-473, August.
    13. Hellwig, Martin & Leininger, Wolfgang, 1987. "On the existence of subgame-perfect equilibrium in infinite-action games of perfect information," Journal of Economic Theory, Elsevier, vol. 43(1), pages 55-75, October.
    14. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2016. "Equilibrium existence for large perfect information games," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 5-18.
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    Cited by:

    1. János Flesch & P. Jean-Jacques Herings & Jasmine Maes & Arkadi Predtetchinski, 2022. "Individual upper semicontinuity and subgame perfect $$\epsilon $$ ϵ -equilibria in games with almost perfect information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 695-719, April.
    2. 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.
    3. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2021. "Multi-lateral strategic bargaining without stationarity," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    4. Kutay Cingiz & János Flesch & P. Jean-Jacques Herings & Arkadi Predtetchinski, 2020. "Perfect information games where each player acts only once," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(4), pages 965-985, June.

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    More about this item

    Keywords

    Backwards induction; Subgame perfection; Equilibrium existence; Large extensive form games; Perfect information;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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