Abstract
Recently, Hazan and Krauthgamer showed [12] that if, for a fixed small ε, an ε-best ε-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 ε. In this paper, we extend their result to show that if an ε-best ε-approximate equilibrium can be efficiently found for arbitrarily small ε > 0, then one can detect the presence of a planted clique of size (2 + δ) logn in G n, 1/2 in polynomial time for arbitrarily small δ > 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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Minder, L., Vilenchik, D. (2009). Small Clique Detection and Approximate Nash Equilibria. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2009 2009. Lecture Notes in Computer Science, vol 5687. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03685-9_50
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DOI: https://doi.org/10.1007/978-3-642-03685-9_50
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