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In a system where noncooperative agents share a common resource, we propose the price of anarchy, which is the ratio between the worst possible Nash equilibrium and the social optimum, as a measure of the effectiveness of the system. Deriving upper and lower bounds for this ratio in a model where several agents share a very simple network leads to some(More)
We consider the price of anarchy of pure Nash equilibria in congestion games with linear latency functions. For asymmetric games, the price of anarchy of maximum social cost is Θ(√N), where N is the number of players. For all other cases of symmetric or asymmetric games and for both maximum and average social cost, the price of anarchy is 5/2. We(More)
We propose a plausible explanation of the power law distributions of degrees observed in the graphs arising in the Internet topology [Faloutsos, Faloutsos, and Faloutsos, SIGCOMM 1999] based on a toy model of Internet growth in which two objectives are optimized simultaneously: " last mile " connection costs, and transmission delays measured in hops. We(More)
We study the mechanism design problem of scheduling tasks on <i>n</i> unrelated machines in which the machines are the players of the mechanism. The problem was proposed and studied in the seminal paper of Nisan and Ronen, where it was shown that the approximation ratio of mechanisms is between 2 and <i>n</i>. We improve the lower bound to 1 + &radic;2 for(More)
We prove that the <italic>work function algorithm</italic> for the <italic>k</italic>-server problem has a competitive ratio at most 2<italic>k</italic>&minus;1. Manasse et al. [1988] conjectured that the competitive ratio for the <italic>k</italic>-server problem is exactly <italic>k</italic> (it is trivially at least <italic>k</italic>); previously the(More)
We introduce the notion of coordination mechanisms to improve the performance in systems with independent selfish agents. The quality of a coordination mechanism is measured by its price of anarchy—the worst-case performance of a Nash equilibrium over the (centrally controlled) social optimum. We give upper and lower bounds for the price of anarchy for(More)
We consider the price of stability for Nash and correlated equilibria of linear congestion games. The price of stability is the optimistic price of anarchy, the ratio of the cost of the best Nash or correlated equilibrium over the social optimum. We show that for the sum social cost, which corresponds to the average cost of the players, every linear(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)