Abstract
Recently, Hazan and Krauthgamer showed [12] that if, for a fixed small *** , an *** -best *** -approximate Nash equilibrium can be found in polynomial time in two-player games, then it is also possible to find a planted clique in G n , 1/2 of size C logn , where C is a large fixed constant independent of *** . In this paper, we extend their result to show that if an *** -best *** -approximate equilibrium can be efficiently found for arbitrarily small *** > 0, then one can detect the presence of a planted clique of size (2 + *** ) logn in G n , 1/2 in polynomial time for arbitrarily small *** > 0. Our result is optimal in the sense that graphs in G n , 1/2 have cliques of size (2 *** o (1)) logn with high probability.
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