Approximate Plutocratic and Egalitarian Nash Equilibria
نویسندگان
چکیده
We pose the problem of computing approximate Nash equilibria in bimatrix games with two simultaneous criteria of optimization: minimization of the incentives to deviate from a strategy profile and maximization of a measure of quality of the strategy profile. We consider two natural measures of quality: the maximum and the minimum of the payoffs of the two players. Maximizing the former yields plutocratic Nash equilibria, and maximizing the latter yields egalitarian Nash equilibria. We give polynomial-time algorithms that compute ε-Nash equilibria for ε ≥ 3− √ 5 2 ≈ 0.382, and that approximate the quality of plutocratic and egalitarian Nash equilibria to various degrees.
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