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- W2509191640 abstract "We study the problem of finding approximate Nash equilibria that satisfy certain conditions, such as providing good social welfare. In particular, we study the problem $$epsilon $$ -NE $$delta $$ -SW: find an $$epsilon $$ -approximate Nash equilibrium ( $$epsilon $$ -NE) that is within $$delta $$ of the best social welfare achievable by an $$epsilon $$ -NE. Our main result is that, if the randomized exponential-time hypothesis (RETH) is true, then solving $$left( frac{1}{8} - mathrm {O}(delta )right) $$ -NE $$mathrm {O}(delta )$$ -SW for an $$ntimes n$$ bimatrix game requires $$n^{mathrm {widetilde{Omega }}(delta ^{varLambda } log n)}$$ time, where $$varLambda $$ is a constant. Building on this result, we show similar conditional running time lower bounds on a number of decision problems for approximate Nash equilibria that do not involve social welfare, including maximizing or minimizing a certain player’s payoff, or finding approximate equilibria contained in a given pair of supports. We show quasi-polynomial lower bounds for these problems assuming that RETH holds, and these lower bounds apply to $$epsilon $$ -Nash equilibria for all $$epsilon < frac{1}{8}$$ . The hardness of these other decision problems has so far only been studied in the context of exact equilibria." @default.
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- W2509191640 date "2016-01-01" @default.
- W2509191640 modified "2023-09-23" @default.
- W2509191640 title "Inapproximability Results for Approximate Nash Equilibria" @default.
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- W2509191640 doi "https://doi.org/10.1007/978-3-662-54110-4_3" @default.
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