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The Complexity of Computing Equilibria

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  • Papadimitriou, Christos

Abstract

In one of the most influential existence theorems in mathematics, John F. Nash proved in 1950 that any normal form game has an equilibrium. More than five decades later, it was shown that the computational task of finding such an equilibrium is intractable, that is, unlikely to be carried out within any feasible time limits for large enough games. This chapter develops the necessary background and formalism from the theory of algorithms and complexity developed in computer science, in order to understand this result, its context, its proof, and its implications.

Suggested Citation

  • Papadimitriou, Christos, 2015. "The Complexity of Computing Equilibria," Handbook of Game Theory with Economic Applications,, Elsevier.
    • Handle: RePEc:eee:gamchp:v:4:y:2015:i:c:p:779-810
    DOI: 10.1016/B978-0-444-53766-9.00014-8
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    References listed on IDEAS

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    Cited by:

    1. Agha Mohammad Ali Kermani, Mehrdad & Fatemi Ardestani, Seyed Farshad & Aliahmadi, Alireza & Barzinpour, Farnaz, 2017. "A novel game theoretic approach for modeling competitive information diffusion in social networks with heterogeneous nodes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 570-582.
    2. Nicola, Gatti & Mario, Gilli & Fabio, Panozzo, 2016. "Further results on verification problems in extensive-form games," Working Papers 347, University of Milano-Bicocca, Department of Economics, revised 15 Jul 2016.
    3. Ilan Nehama, 2016. "Analyzing Games with Ambiguous Player Types Using the MINthenMAX Decision Model," Discussion Paper Series dp700, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.

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    More about this item

    Keywords

    Normal form games; Nash equilibrium; Algorithms; Computational complexity; Polynomial-time algorithms; NP-complete problems; PPAD-complete problems;
    All these keywords.

    JEL classification:

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

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