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In this paper we propose a new methodology for determining approximate Nash equilibria of non-cooperative bimatrix games and, based on that, we provide an efficient algorithm that computes 0.3393-approximate equilibria, the best approximation till now. The methodology is based on the formulation of an appropriate function of pairs of mixed strategies… (More)

What is the price of anarchy when unsplittable demands are routed selfishly in general networks with load-dependent edge delays? Motivated by this question we generalize the model of [14] to the case of weighted congestion games. We show that varying demands of users crucially affect the nature of these games, which are no longer isomorphic to exact… (More)

The classical occupancy problem is concerned with studying the number of empty bins resulting from a random allocation of m balls to n bins. We provide a series of tail bounds on the distribution of the number of empty bins. These tail bounds should find application in randomized algorithms and probabilistic analysis. Our motivating application is the… (More)

In this work, we study the combinatorial structure and the computational complexity of Nash equilibria for a certain game that models selfish routing over a network consisting of m parallel links. We assume a collection of n users, each employing a mixed strategy, which is a probability distribution over links, to control the routing of its own assigned… (More)

1 PROBLEM DEFINITION Nash [13] introduced the concept of Nash equilibria in non-cooperative games and proved that any game possesses at least one such equilibrium. A well-known algorithm for computing a Nash equilibrium of a 2-player game is the Lemke-Howson algorithm [11], however it has exponential worst-case running time in the number of available pure… (More)

We consider selfish routing over a network consisting of m parallel links through which n selfish users route their traffic trying to minimize their own expected latency. We study the class of mixed strategies in which the expected latency through each link is at most a constant multiple of the optimum maximum latency had global regulation been available.… (More)