Years and Authors of Summarized Original Work
2006; Chen, Deng
Problem Definition
In the middle of the last century, Nash [8] studied general noncooperative games and proved that there exists a set of mixed strategies, now commonly referred to as a Nash equilibrium, one for each player, such that no player can benefit if he/she changes his/her own strategy unilaterally. Since the development of Nash’s theorem, researchers have worked on how to compute Nash equilibria efficiently. Despite much effort in the last half century, no significant progress has been made on characterizing its algorithmic complexity, though both hardness results and algorithms have been developed for various modified versions.
An exciting breakthrough, which shows that computing Nash equilibria is possibly hard, was made by Daskalakis, Goldberg, and Papadimitriou [5], for games among four players or more. The problem was proven to be complete in PPAD(polynomial parity argument, directed version), a complexity...
Recommended Reading
Chen X, Deng X (2005) 3-Nash is ppad-complete. ECCC, TR05-134
Chen X, Deng X (2006) Settling the complexity of two-player Nash-equilibrium. In: Proceedings of the 47th annual IEEE symposium on foundations of computer science (FOCS’06), Berkeley, pp 261–272
Chen X, Deng X, Teng SH (2006) Computing Nash equilibria: approximation and smoothed complexity. In: Proceedings of the 47th annual IEEE symposium on foundations of computer science (FOCS’06), Berkeley, pp 603–612
Daskalakis C, Papadimitriou CH (2005) Three-player games are hard. ECCC, TR05-139
Daskalakis C, Goldberg PW, Papadimitriou CH (2006) The complexity of computing a Nash equilibrium. In: Proceedings of the 38th ACM symposium on theory of computing (STOC’06), Seattle, pp 71–78
Goldberg PW, Papadimitriou CH (2006) Reducibility among equilibrium problems. In: Proceedings of the 38th ACM symposium on theory of computing (STOC’06), Seattle, pp 61–70
Megiddo N, Papadimitriou CH (1991) On total functions, existence theorems and computational complexity. Theor Comput Sci 81:317–324
Nash JF (1950) Equilibrium point in n-person games. Proc Natl Acad USA 36(1):48–49
Papadimitriou CH (1994) On the complexity of the parity argument and other inefficient proofs of existence. J Comput Syst Sci 48:498–532
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Chen, X. (2015). Complexity of Bimatrix Nash Equilibria. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27848-8_79-3
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DOI: https://doi.org/10.1007/978-3-642-27848-8_79-3
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Latest
Complexity of Bimatrix Nash Equilibria- Published:
- 30 May 2015
DOI: https://doi.org/10.1007/978-3-642-27848-8_79-3
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Original
Complexity of Bimatrix Nash Equilibria- Published:
- 25 November 2014
DOI: https://doi.org/10.1007/978-3-642-27848-8_79-2