Abstract
We introduce and study satisfiability games, a new class of games that can be seen as the non-cooperative version of classical maximum satisfiability problems. We give several results involving these games and mainly focus on their expressiveness. In particular, we show that there exists a strong correspondence between satisfiability games and congestion games. As one of the consequences of our results, we show that each game is isomorphic to a congestion game with player specific payoffs. Thus, each other game can be defined as a particular specialization of congestion games with player specific payoffs and this paper can be considered as a first effort in outlining a classification of non-cooperative games.
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References
Anshelevich, E., Dasgupta, A., Tardos, E., Wexler, T.: Near-Optimal Network Design with Selfish Agents. In: Proceedings of STOC 2003, pp. 511–520. ACM Press, New York (2003)
Chen, X., Deng, X.: Settling the Complexity of 2-Player Nash Equilibrium. In: Proceedings of FOCS 2006, pp. 261–272. IEEE Computer Society Press, Los Alamitos (2006)
Christodoulou, G., Koutsoupias, E., Nanavati, A.: Coordination Mechanisms. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 345–357. Springer, Heidelberg (2004)
Christodoulou, G., Mirrokni, V.S., Sidiropoulos, A.: Convergence and Approximation in Potential Games. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 349–360. Springer, Heidelberg (2006)
Daskalakis, K., Goldberg, P.W., Papadimitriou, C.H.: The Complexity of Computing a Nash Equilibrium. In: Proceedings of STOC 2006, pp. 71–78. ACM Press, New York (2006)
Daskalakis, K., Papadimitriou, C.H.: Three-Player Games Are Hard. Technical Report TR05-139, ECCC (2005)
Fabrikant, A., Papadimitriou, C.H., Talwar, K.: The Complexity of Pure Nash Equilibria. In: Proceedings of STOC 2004, pp. 604–612. ACM Press, New York (2004)
Korilis, Y., Lazar, A.: On the Existence of Equilibria in Non-cooperative Optimal Flow Control. Journal of the ACM 42(3), 584–613 (1995)
Koutsoupias, E., Papadimitriou, C.H.: Worst-case Equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)
La, R., Anantharam, V.: Optimal Routing Control: Game Theoretic Approach. In: Proceedings of the 1997 CDC Conference (1997)
Milchtaich, I.: Congestion Games with Player Specific Payoff Functions. Games and Economic Behavior 13, 111–124 (1996)
Mirrokni, V.S.: Approximation Algorithms for Distributed and Selfish Agents. Massachusetts Institute of Technology (June 2005)
Mirrokni, V.S., Vetta, A.: Convergence Issues in Competitive Games. In: Jansen, K., Khanna, S., Rolim, J.D.P., Ron, D. (eds.) RANDOM 2004 and APPROX 2004. LNCS, vol. 3122, pp. 183–194. Springer, Heidelberg (2004)
Monderer, D.: Multipotential Games. In: Proceedings of IJCAI, to appear (2007)
Monderer, D., Shapley, L.S.: Potential Games. Games and Economic Behavior 14, 124–143 (1996)
Nash, J.: Equilibrium Points in n-person Games. Proceedings of the National Academy of Sciences 36, 48–49 (1950)
Nash, J.: Non-cooperative Games. Annals of Mathematics 54(2), 286–295 (1951)
Rosenthal, R.W.: A Class of Games Possessing Pure-Strategy Nash Equilibria. International Journal of Game Theory 2, 65–67 (1973)
Shenker, S.J.: Making Greed Work in Networks: a Game-Theoretic Analysis of Switch Service Disciplines. IEEE/ACM Transactions on Networking 3(6), 819–831 (1995)
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Bilò, V. (2007). On Satisfiability Games and the Power of Congestion Games. In: Kao, MY., Li, XY. (eds) Algorithmic Aspects in Information and Management. AAIM 2007. Lecture Notes in Computer Science, vol 4508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72870-2_22
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DOI: https://doi.org/10.1007/978-3-540-72870-2_22
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