Abstract
In this paper we present an implementation and performance evaluation of a descent algorithm that was proposed in [1] for the computation of approximate Nash equilibria of non-cooperative bi-matrix games. This algorithm, which achieves the best polynomially computable ε-approximate equilibria till now, is applied here to several problem instances designed so as to avoid the existence of easy solutions. Its performance is analyzed in terms of quality of approximation and speed of convergence. The results demonstrate significantly better performance than the theoretical worst case bounds, both for the quality of approximation and for the speed of convergence. This motivates further investigation into the intrinsic characteristics of descent algorithms applied to bi-matrix games. We discuss these issues and provide some insights about possible variations and extensions of the algorithmic concept that could lead to further understanding of the complexity of computing equilibria. We also prove here a new significantly better bound on the number of loops required for convergence of the descent algorithm.
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Tsaknakis, H., Spirakis, P.G.: An Optimization Approach for Approximate Nash Equilibria. In: Deng, X., Graham, F.C. (eds.) WINE 2007. LNCS, vol. 4858, pp. 42–56. Springer, Heidelberg (2007)
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.G.: Efficient algorithms for constant well supported approximate equilibria of bimatrix games. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596. Springer, Heidelberg (2007)
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 Comp. Soc. Press, Los Alamitos (2006)
Daskalakis, C., Mehta, A., Papadimitriou, C.: Progress in approximate nash equilibrium. In: Proc. Of the 8th ACM Conf. on Electr. Commerce (EC 2007) (2007)
Daskalakis, C., Mehta, A., Papadimitriou, C.: A note on approximate nash equilibria. In: Spirakis, P.G., Mavronicolas, M., Kontogiannis, S.C. (eds.) WINE 2006. LNCS, vol. 4286, pp. 297–306. Springer, Heidelberg (2006)
Boss, H., Byrka, J., Markakis, E.: New Algorithms for Approximate Nash Equilibria in Bimatrix Games. In: Deng, X., Graham, F.C. (eds.) WINE 2007. LNCS, vol. 4858, pp. 17–29. Springer, Heidelberg (2007)
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Tsaknakis, H., Spirakis, P.G., Kanoulas, D. (2008). Performance Evaluation of a Descent Algorithm for Bi-matrix Games. In: Papadimitriou, C., Zhang, S. (eds) Internet and Network Economics. WINE 2008. Lecture Notes in Computer Science, vol 5385. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92185-1_29
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DOI: https://doi.org/10.1007/978-3-540-92185-1_29
Publisher Name: Springer, Berlin, Heidelberg
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