Abstract
We analyze the problem of computing a correlated equilibrium that optimizes some objective (e.g., social welfare). Papadimitriou and Roughgarden [2008] gave a sufficient condition for the tractability of this problem; however, this condition only applies to a subset of existing representations. We propose a different algorithmic approach for the optimal CE problem that applies to all compact representations, and give a sufficient condition that generalizes that of Papadimitriou and Roughgarden [2008]. In particular, we reduce the optimal CE problem to the deviation − adjusted social welfare problem, a combinatorial optimization problem closely related to the optimal social welfare problem. This framework allows us to identify new classes of games for which the optimal CE problem is tractable; we show that graphical polymatrix games on tree graphs are one example. We also study the problem of computing the optimal coarse correlated equilibrium, a solution concept closely related to CE. Using a similar approach we derive a sufficient condition for this problem, and use it to prove that the problem is tractable for singleton congestion games.
All proofs are omitted in this extended abstract. A full version is available at http://arxiv.org/abs/1109.6064
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aumann, R.: Subjectivity and correlation in randomized strategies. Journal of Mathematical Economics 1(1), 67–96 (1974)
Aumann, R.: Correlated equilibrium as an expression of Bayesian rationality. Econometrica: Journal of the Econometric Society, 1–18 (1987)
Bhat, N., Leyton-Brown, K.: Computing Nash equilibria of action-graph games. In: UAI: Proceedings of the Conference on Uncertainty in Artificial Intelligence, pp. 35–42 (2004)
Blum, B., Shelton, C., Koller, D.: A continuation method for Nash equilibria in structured games. JAIR: Journal of Artificial Intelligence Research 25, 457–502 (2006)
Chen, X., Deng, X.: Settling the complexity of 2-player Nash-equilibrium. In: FOCS: Proceedings of the Annual IEEE Symposium on Foundations of Computer Science, pp. 261–272 (2006)
Daskalakis, C., Fabrikant, A., Papadimitriou, C.: The Game World is Flat: The Complexity of Nash Equilibria in Succinct Games. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4051, pp. 513–524. Springer, Heidelberg (2006)
Daskalakis, C., Papadimitriou, C.: Three-player games are hard. In: ECCC, TR05-139 (2005)
Goldberg, P.W., Papadimitriou, C.H.: Reducibility among equilibrium problems. In: STOC: Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 61–70 (2006)
Hannan, J.: Approximation to Bayes risk in repeated plays. In: Dresher, M., Tucker, A., Wolfe, P. (eds.) Contributions to the Theory of Games, vol. 3, pp. 97–139. Princeton University Press (1957)
Ieong, S., McGrew, R., Nudelman, E., Shoham, Y., Sun, Q.: Fast and compact: A simple class of congestion games. In: AAAI: Proceedings of the AAAI Conference on Artificial Intelligence, pp. 489–494 (2005)
Jiang, A., Leyton-Brown, K.: Polynomial computation of exact correlated equilibrium in compact games. In: EC: Proceedings of the ACM Conference on Electronic Commerce (2011), http://arxiv.org/abs/1011.0253
Jiang, A.X., Leyton-Brown, K., Bhat, N.: Action-graph games. Games and Economic Behavior 71(1), 141–173 (2011)
Kamisetty, H., Xing, E.P., Langmead, C.J.: Approximating correlated equilibria using relaxations on the marginal polytope. In: ICML (2011)
Kearns, M., Littman, M., Singh, S.: Graphical models for game theory. In: UAI: Proceedings of the Conference on Uncertainty in Artificial Intelligence, pp. 253–260 (2001)
Leyton-Brown, K., Tennenholtz, M.: Local-effect games. In: IJCAI: Proceedings of the International Joint Conference on Artificial Intelligence, pp. 772–780 (2003)
Nisan, N., Ronen, A.: Algorithmic mechanism design. Games and Economic Behavior 35, 166–196 (2001)
Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V. (eds.): Algorithmic game theory. Cambridge University Press, Cambridge (2007)
Papadimitriou, C.: Computing correlated equilibria in multiplayer games. In: STOC: Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 49–56 (2005)
Papadimitriou, C., Roughgarden, T.: Computing correlated equilibria in multi-player games. Journal of the ACM 55(3), 14 (2008)
Rosenthal, R.: A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory 2, 65–67 (1973)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jiang, A.X., Leyton-Brown, K. (2011). A General Framework for Computing Optimal Correlated Equilibria in Compact Games. In: Chen, N., Elkind, E., Koutsoupias, E. (eds) Internet and Network Economics. WINE 2011. Lecture Notes in Computer Science, vol 7090. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25510-6_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-25510-6_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25509-0
Online ISBN: 978-3-642-25510-6
eBook Packages: Computer ScienceComputer Science (R0)