Performance Evaluation of a Descent Algorithm for Bi-matrix Games

  • Authors:

  • Haralampos Tsaknakis;Paul G. Spirakis;Dimitrios Kanoulas

  • Affiliations:

  • Research Academic Computer Technology Institute (RACTI), Greece;Research Academic Computer Technology Institute (RACTI), Greece and Dept. of Computer Eng. and Informatics, Patras University, Patras, Greece;Dept. of Computer Eng. and Informatics, Patras University, Patras, Greece

  • Venue:
  • WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
  • Year:
  • 2008

Quantified Score

Hi-index 0.00

Visualization

Abstract

In this paper we present an implementation and performanceevaluation of a descent algorithm that was proposed in [1] for thecomputation of approximate Nash equilibria of non-cooperativebi-matrix games. This algorithm, which achieves the bestpolynomially computable ε-approximate equilibria till now,is applied here to several problem instances designed so as toavoid the existence of easy solutions. Its performance is analyzedin terms of quality of approximation and speed of convergence. Theresults demonstrate significantly better performance than thetheoretical worst case bounds, both for the quality ofapproximation and for the speed of convergence. This motivatesfurther investigation into the intrinsic characteristics of descentalgorithms applied to bi-matrix games. We discuss these issues andprovide some insights about possible variations and extensions ofthe algorithmic concept that could lead to further understanding ofthe complexity of computing equilibria. We also prove here a newsignificantly better bound on the number of loops required forconvergence of the descent algorithm.