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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)

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)

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)

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)

In this paper, we analyze the stability properties of the FIFO protocol in the Adversarial Queueing model for packet routing. We show a graph for which FIFO is stable for any adversary with injection rate <i>r</i> ≰ 0.1428. We generalize this results to show upper bound for stability of any network under FIFO protocol, answering partially an open… (More)

In this work we study the tractability of well supported approximate Nash Equilibria (SuppNE in short) in bimatrix games. In view of the apparent intractability of constructing Nash Equilibria (NE in short) in polynomial time, even for bimatrix games, understanding the limitations of the approximability of the problem is of great importance. We initially… (More)