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A Counterexample to the Fully Mixed Nash Equilibrium Conjecture

We study a well-known resource allocation game introduced by Koutsoupias and Papadimitriou. It was conjectured by Gairing et al. that the fully mixed Nash equilibrium is the worst Nash equilibrium for this game. The known algorithms for approxaimting the so-called “price of anarchy” wrt mixed equilibria rely on this conjecture. We present a counterexample to the conjecture showing that fully mixed equilibria cannot be used to approximate the price of anarchy within reasonable factors.