Abstract
We focus on the problem of computing an ε-Nash equilibrium of a bimatrix game, when ε is an absolute constant. We present a simple algorithm for computing a \(\frac{3}{4}\)-Nash equilibrium for any bimatrix game in strongly polynomial time and we next show how to extend this algorithm so as to obtain a (potentially stronger) parameterized approximation. Namely, we present an algorithm that computes a \(\frac{2+\lambda}{4}\)-Nash equilibrium, where λ is the minimum, among all Nash equilibria, expected payoff of either player. The suggested algorithm runs in time polynomial in the number of strategies available to the players.
Partially supported by the Future and Emerging Technologies Unit of EC (IST priority – 6th FP), under contract no. FP6-021235-2 (ARRIVAL) and 015964 “Algorithmic Principles for Building Efficient Overlay Computers”(AEOLUS),and by the General Secretariat for Research and Technology of the Greek Ministry of Development within the programme PENED 2003.
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Kontogiannis, S.C., Panagopoulou, P.N., Spirakis, P.G. (2006). Polynomial Algorithms for Approximating Nash Equilibria of Bimatrix Games. In: Spirakis, P., Mavronicolas, M., Kontogiannis, S. (eds) Internet and Network Economics. WINE 2006. Lecture Notes in Computer Science, vol 4286. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11944874_26
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DOI: https://doi.org/10.1007/11944874_26
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