Abstract
We consider applications of probabilistic techniques in the framework of algorithmic game theory. We focus on three distinct case studies: (i) The exploitation of the probabilistic method to demonstrate the existence of approximate Nash equilibria of logarithmic support sizes in bimatrix games; (ii) the analysis of the statistical conflict that mixed strategies cause in network congestion games; (iii) the effect of coalitions in the quality of congestion games on parallel links.
Partially supported by EU/6th Framework Programme, contract 001907 (DELIS).
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References
Althöfer, I.: On sparse approximations to randomized strategies and convex combinations. Linear Algebra and Applications 199, 339–355 (1994)
Awerbuch, B., Azar, Y., Epstein, A.: The price of routing unsplittable flow. In: Proc. of the 37th ACM Symp. on Th. of Comp (STOC 2005), pp. 57–66. ACM Press, New York (2005)
Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming: Theory and Algorithms, 2nd edn. John Wiley and Sons, Inc, Chichester (1993)
Beckmann, M., McGuire, C.B., Winsten, C.B.: Studies in the Economics of Transportation. Yale University Press (1956)
Chen, X., Deng, X.: Settling the complexity of 2-player nash equilibrium. In: Proc. of the 47th IEEE Symp. on Found. of Comp. Sci (FOCS 2006), pp. 261–272. IEEE Computer Society Press, Los Alamitos (2006)
Chen, X., Deng, X., Teng, S.H.: Computing nash equilibria: Approximation and smoothed complexity. In: Proc. of the 47th IEEE Symp. on Found. of Comp. Sci (FOCS 2006), pp. 603–612. IEEE Computer Society Press, Los Alamitos (2006)
Christodoulou, G., Koutsoupias, E.: The Price of Anarchy of Finite Congestion Games. In: Proc. of the 37th ACM Symp. on Th. of Comp (STOC 2005), pp. 67–73. ACM Press, New York (2005)
Daskalakis, C., Mehta, A., Papadimitriou, C.: A note on approximate equilibria. In: Spirakis, P.G., Mavronicolas, M., Kontogiannis, S.C. (eds.) WINE 2006. LNCS, vol. 4286, pp. 297–306. Springer, Heidelberg (2006)
Dorn, W.S.: Duality in quadratic programming. Quarterly of Applied Mathematics 18(2), 155–162 (1960)
Dubhashi, D., Ranjan, D.: Balls and bins: A study in negative dependence. Random Structures & Algorithms 13(2), 99–124 (1998)
Fabrikant, A., Papadimitriou, C., Talwar, K.: The complexity of pure nash equilibria. In: Proc. of the 36th ACM Symp. on Th. of Comp (STOC 2004), ACM Press, New York (2004)
Fotakis, D., Kontogiannis, S., Spirakis, P.: Selfish unsplittable flows. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 226–239. Springer, Heidelberg (2004)
Fotakis, D., Kontogiannis, S., Spirakis, P.: Symmetry in network congestion games: Pure equilibria and anarchy cost. In: Erlebach, T., Persinao, G. (eds.) WAOA 2005. LNCS, vol. 3879, pp. 161–175. Springer, Heidelberg (2006)
Fotakis, D., Kontogiannis, S., Spirakis, P.: Atomic congestion games among coalitions. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4051, pp. 572–583. Springer, Heidelberg (2006)
Hoeffding, W.: Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association 58(301), 13–30 (1963)
Kamath, A., Motwani, R., Palem, K., Spirakis, P.: Tail bounds for occupancy and the satisfiability threshold conjecture. Random Structures & Algorithms 7(1), 59–80 (1995)
Kontogiannis, S., Panagopoulou, P., Spirakis, P.: Polynomial algorithms for approximating nash equilibria in bimatrix games. In: Spirakis, P.G., Mavronicolas, M., Kontogiannis, S.C. (eds.) WINE 2006. LNCS, vol. 4286, pp. 286–296. Springer, Heidelberg (2006)
Kontogiannis, S., Spirakis, P.: Well supported approximate equilibria in bimatrix games: A graph theoretic approach. In: Proc. of the 32nd Int. Symp. on Math. Found. of Comp. Sci (MFCS 2007). LNCS, Springer, Heidelberg (2007), Preliminary version appeared as technical report DELIS-TR-0487 of EU Project DELIS – Dynamically Evolving Large Scale Information Systems (January 2007)
Koutsoupias, E., Mavronicolas, M., Spirakis, P.: Approximate equilibria and ball fusion. Theory of Computing Systems, Special Issue devoted to SIROCCO 2002 36(6), 683–693 (2003)
Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)
Lipton, R., Markakis, E., Mehta, A.: Playing large games using simple strategies. In: Proc. of the 4th ACM Conf. on El. Comm (EC 2003). Assoc. of Comp. Mach., pp. 36–41. ACM Press, New York (2003)
Monderer, D., Shapley, L.: Potential games. Games & Econ. Behavior 14, 124–143 (1996)
Nash, J.: Noncooperative games. Annals of Mathematics 54, 289–295 (1951)
Papadimitriou, C., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Prentice-Hall, Inc., Englewood Cliffs (1982)
Rosenthal, R.W.: A class of games possessing pure-strategy nash equilibria. Int. J. of Game Theory 2, 65–67 (1973)
Roughdarden, T., Tardos, E.: How bad is selfish routing? J. of ACM 49(2), 236–259 (2002)
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Kontogiannis, S.C., Spirakis, P.G. (2007). Probabilistic Techniques in Algorithmic Game Theory. In: Hromkovič, J., Královič, R., Nunkesser, M., Widmayer, P. (eds) Stochastic Algorithms: Foundations and Applications. SAGA 2007. Lecture Notes in Computer Science, vol 4665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74871-7_4
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DOI: https://doi.org/10.1007/978-3-540-74871-7_4
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