Abstract
Game theory in general and the concept of Nash equilibrium in particular have lately come under increased scrutiny by theoretical computer scientists. Computing a mixed Nash equilibrium is a case in point. For many years, one of the most important open problems was the complexity of computing a mixed Nash equilibrium in games with only two players. Only recently was it solved by a sequence of significant papers (Goldberg and Papadimitriou (2006), Daskalakis et.al. (2006), Chen and Deng (2005), Daskalakis and Papadimitriou (2005), and Chen and Deng (2006)).
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References
Anshelevich, E., A. Dasgupta, J. Kleinberg, É. Tardos, T. Wexler, and T. Roughgarden (2004). The price of stability for network design with fair cost allocation. In Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, Rome, Italy, pp. 295–304.
Chen, X. and X. Deng (2005). 3-Nash is PPAD-complete. Electronic Colloquium on Computational Complexity TR05-134.
Chen, X. and X. Deng (2006). Settling the complexity of 2-player Nashequilibrium. In Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science, Berkeley, CA, to appear.
Daskalakis, C., P. Goldberg, and C. Papadimitriou (2006). The complexity of computing a Nash equilibrium. In Proceedings of the 38th Annual ACM Symposium on Theory of Computing, Seattle, WA, pp. 71–78.
Daskalakis, C. and C. Papadimitriou (2005). Three-player games are hard. Electronic Colloquium on Computational Complexity TR05-139.
Dunkel, J. (2005). The Complexity of Pure-Strategy Nash Equilibria in Non-Cooperative Games. Diplomarbeit, Institute of Mathematics, Technische Universität Berlin, Germany, July 2005.
Fotakis, D., S. Kontogiannis, and P. Spirakis (2005). Selfish unsplittable flows. Theoretical Computer Science 348, pp. 226–239.
Goldberg, P. and C. Papadimitriou (2006). Reducibility among equilibrium problems. In Proceedings of the 38th Annual ACM Symposium on Theory of Computing, Seattle, WA, pp. 61–70.
Leyton-Brown, K. and M. Tennenholtz (2003). Local-effect games. In Proceedings of the 18th International Joint Conference on Artificial Intelligence, Acapulco, Mexico, pp. 772–780.
Nash, J. (1951). Non-cooperative games. Annals of Mathematics 54, 268–295.
Rosenthal, R. (1973). A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory 2, pp. 65–67.
Schäffer, A. and M. Yannakakis (1991). Simple local search problems that are hard to solve. SIAM Journal on Computing 20, pp. 56–87.
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Dunke, J. (2007). Complexity of Pure-Strategy Nash Equilibria in Non-Cooperative Games. In: Waldmann, KH., Stocker, U.M. (eds) Operations Research Proceedings 2006. Operations Research Proceedings, vol 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69995-8_7
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DOI: https://doi.org/10.1007/978-3-540-69995-8_7
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