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- W2806555090 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 ϵ-NE δ-SW: find an ϵ-approximate Nash equilibrium (ϵ-NE) that is within δ of the best social welfare achievable by an ϵ-NE. Our main result is that, if the exponential-time hypothesis (ETH) is true, then solving (18−O(δ))-NE O(δ)-SW for an n×n bimatrix game requires nΩ˜(logn) time. Building on this result, we show similar conditional running time lower bounds for a number of other decision problems for ϵ-NE, where, for example, the payoffs or supports of players are constrained. We show quasi-polynomial lower bounds for these problems assuming ETH, where these lower bounds apply to ϵ-Nash equilibria for all ϵ<18. The hardness of these other decision problems has so far only been studied in the context of exact equilibria." @default.
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- W2806555090 date "2018-10-01" @default.
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- W2806555090 title "Inapproximability results for constrained approximate Nash equilibria" @default.
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- W2806555090 doi "https://doi.org/10.1016/j.ic.2018.06.001" @default.
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