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The complexity of computing a (quasi-)perfect equilibrium for an n-player extensive form game

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  • Etessami, Kousha

Abstract

We study the complexity of computing or approximating refinements of Nash equilibrium for finite n-player extensive form games of perfect recall (EFGPR), n≥3. Our results apply to a number of well-studied refinements, including sequential equilibrium, extensive-form perfect equilibrium, and quasi-perfect equilibrium.

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  • Etessami, Kousha, 2021. "The complexity of computing a (quasi-)perfect equilibrium for an n-player extensive form game," Games and Economic Behavior, Elsevier, vol. 125(C), pages 107-140.
    • Handle: RePEc:eee:gamebe:v:125:y:2021:i:c:p:107-140
    DOI: 10.1016/j.geb.2019.03.006
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    1. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    2. Robert Wilson, 1972. "Computing Equilibria of Two-Person Games from the Extensive Form," Management Science, INFORMS, vol. 18(7), pages 448-460, March.
    3. Mertens, J.-F., 1995. "Two examples of strategic equilibrium," Games and Economic Behavior, Elsevier, vol. 8(2), pages 378-388.
    4. Blume, Lawrence E & Zame, William R, 1994. "The Algebraic Geometry of Perfect and Sequential Equilibrium," Econometrica, Econometric Society, vol. 62(4), pages 783-794, July.
    5. Von Stengel, Bernhard, 2002. "Computing equilibria for two-person games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 45, pages 1723-1759, Elsevier.
    6. Gilboa, Itzhak & Zemel, Eitan, 1989. "Nash and correlated equilibria: Some complexity considerations," Games and Economic Behavior, Elsevier, vol. 1(1), pages 80-93, March.
    7. von Stengel, Bernhard, 1996. "Efficient Computation of Behavior Strategies," Games and Economic Behavior, Elsevier, vol. 14(2), pages 220-246, June.
    8. Bernhard von Stengel & Antoon van den Elzen & Dolf Talman, 2002. "Computing Normal Form Perfect Equilibria for Extensive Two-Person Games," Econometrica, Econometric Society, vol. 70(2), pages 693-715, March.
    9. Herbert E. Scarf, 1967. "The Approximation of Fixed Points of a Continuous Mapping," Cowles Foundation Discussion Papers 216R, Cowles Foundation for Research in Economics, Yale University.
    10. Yamamoto, Yoshitsugu, 1993. "A Path-Following Procedure to Find a Proper Equilibrium of Finite Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(3), pages 249-259.
    11. van Damme, E.E.C., 1984. "A relation between perfect equilibria in extensive form games and proper equilibria in normal form games," Other publications TiSEM 3734d89e-fd5c-4c80-a230-5, Tilburg University, School of Economics and Management.
    12. Koller, Daphne & Megiddo, Nimrod & von Stengel, Bernhard, 1996. "Efficient Computation of Equilibria for Extensive Two-Person Games," Games and Economic Behavior, Elsevier, vol. 14(2), pages 247-259, June.
    13. Carlos Pimienta & Jianfei Shen, 2014. "On the equivalence between (quasi-)perfect and sequential equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 395-402, May.
    14. Peter Miltersen & Troels Sørensen, 2010. "Computing a quasi-perfect equilibrium of a two-player game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 175-192, January.
    15. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    16. repec:cup:cbooks:9781316779309 is not listed on IDEAS
    17. McKelvey, Richard D. & McLennan, Andrew, 1996. "Computation of equilibria in finite games," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 2, pages 87-142, Elsevier.
    18. Roughgarden,Tim, 2016. "Twenty Lectures on Algorithmic Game Theory," Cambridge Books, Cambridge University Press, number 9781316624791.
    19. Roughgarden,Tim, 2016. "Twenty Lectures on Algorithmic Game Theory," Cambridge Books, Cambridge University Press, number 9781107172661.
    20. Koller, Daphne & Megiddo, Nimrod, 1992. "The complexity of two-person zero-sum games in extensive form," Games and Economic Behavior, Elsevier, vol. 4(4), pages 528-552, October.
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    2. Cao, Yiyin & Dang, Chuangyin, 2022. "A variant of Harsanyi's tracing procedures to select a perfect equilibrium in normal form games," Games and Economic Behavior, Elsevier, vol. 134(C), pages 127-150.

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    More about this item

    Keywords

    Extensive form game; Perfect equilibrium; Quasi-perfect equilibrium; Algorithms; Computational complexity;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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