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arXiv · 1204.0707

Approximate Well-supported Nash Equilibria below Two-thirds

John Fearnley·Paul W. Goldberg·Rahul Savani·Troels Bjerre Sørensen
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Abstract

In an epsilon-Nash equilibrium, a player can gain at most epsilon by changing his behaviour. Recent work has addressed the question of how best to compute epsilon-Nash equilibria, and for what values of epsilon a polynomial-time algorithm exists. An epsilon-well-supported Nash equilibrium (epsilon-WSNE) has the additional requirement that any strategy that is used with non-zero probability by a player must have payoff at most epsilon less than the best response. A recent algorithm of Kontogiannis and Spirakis shows how to compute a 2/3-WSNE in polynomial time, for bimatrix games. Here we introduce a new technique that leads to an improvement to the worst-case approximation guarantee.

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John Fearnley, Paul W. Goldberg, Rahul Savani, Troels Bjerre Sørensen. 2012-04-03. Approximate Well-supported Nash Equilibria below Two-thirds. https://arxiv.org/abs/1204.0707

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