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..., ¸ = x¤=v satis¯es `¤(¸v) = `(v), as required. Hence, the anarchy value ®(L) := sup`2L ®(`) of a class L is equal to (1 ¡ º(L)) ¡1. Therefore, Theorem 3.5 not only implies Roughgarden's main result (=-=Roughgarden 2002-=-, Theorem 3.8) but also extends it to functions ` that are not necessarily di®erentiable and that do not necessarily satisfy that x `(x) is a convex function of x. Moreover, it does not matter if arcs...

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...ers—games in which optimization by individuals approximately optimizes the social good, in spite of the lack of coordination between players. Our results extend previous work on traffic routing game=-=s [16, 17, 18]. -=-1 Introduction Equilibria in noncooperative games are typically inefficient, as illustrated by the classical Prisoner’s Dilemma [13]. In this paper, we aim to quantify this inefficiency by comparing...

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... models. In various papers, researchers have investigated the “price of anarchy,” which is the degradation of a globally optimal solution if the individuals of the network perform in a selfish manner =-=[23, 24]-=-. In this paper, we analyze the degradation of a globally optimal solution if each individual’s knowledge is restricted to its neighborhood or local environment. We hope that this paper makes a step t...

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...ibrium—a “stable point” in which no traffic has an incentive to unilaterally alter its strategy (i.e., its route from s to t). 1 In several previous papers on selfish routing (without taxes), such as =-=[37, 39]-=-, the terms total latency and cost were used synonymously. 6 e∈E e∈EsWe also assume that all agents seek to minimize the sum of the latency experienced and the tax paid. 2 We therefore expect that, in...

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... behavior with respect to the centralized, social welfare-maximizing solution. The price of anarchy has received much attention in games dealing with various networking issues, such as load balancing =-=[7, 21]-=-, routing [20], and flow control [9]. This paper is part of a growing body of literature [10, 3, 2, 6] that studies the price of anarchy in network design, where individuals decide whether or not to f...

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...nd Fotakis et al. [10] have showed that the same bound holds in layered networks as well. The price of anarchy for the total flow latency was considered by Roughgarden and Tardos [23] and Roughgarden =-=[21]-=- in general networks. They obtained tight bounds assuming non-atomic agents, where actions of an individual agent has negligible impact on others. Roughgarden [22] extends these results to an atomic s...

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...hted is precisely JSFP with Inertia. 4.3 Incorporating Tolls to Minimize the Total Congestion It is well known that a Nash equilibrium may not minimize the total congestion experienced by all drivers =-=[33]-=-. In this section, we show how a global planner can minimize the total congestion by implementing tolls on the network. The results are applicable to general congestion games, but we present the appro...