The price of selfish routing

Abstract

We study the problem of routing tra c through a congested network. We focus on the simplest case of a network consisting of m parallel links. W e assume a collection of n network users, each employing a mixed strategy which is a probability distribution over links, to control the shipping of its own assigned tra c. Given a capacity for each link specifying the rate at which the link processes tra c, the objective i s to route tra c so that the maximum expected latency over all links is minimized. We consider both uniform and nonuniform link capacities.How m uch decrease in global performace is necessary due to the absence of some central authority to regulate network tra c and implement an optimal assignment of tra c to links? We i n vestigate this fundamental question in the context of Nash equilibria for such a system, where each n e t work user sel shly routes its tra c only on those links available to it that minimize its expected latency cost, given the network congestion caused by the other users. We use the coordination ratio, de ned by Koutsoupias and Papadimitriou 25] as the ratio of the maximum (over all links) expected latency in the worst possible Nash equlibrium, over the least possible maximum latency had global regulation been available, as a measure of the cost of lack of coordination among the network users.Our point of departure is a set of combinatorial minimum expected latency cost equations, one per network user, that characterize the Nash equilibria of this system. These are linear equations in the minimum expected latencies, involving the users' tra cs, the link capacities and the routing pattern determined by the mixed strategies. In turn, we solve these equations in the case of fully mixed s t r ategies, where each user assigns its tra c with a non-zero probability t o e v ery link, to derive the rst existence and uniqueness results for Nash equilibria in this setting. Most importantly, we use the derived characterizations of Nash equilibria to show, under the assumption of fully mixed strategies, tight upper bounds of no worse than O(ln n= ln ln n) on the coordination ratio for (i) the case of uniform link capacities and arbitrary tra cs, and (ii) the case of non-uniform link capacities and identical tra cs.

Selfish Bin Packing

“…Since then, issues like routing [10,24,28], bandwidth allocation [31], and congestion control [19], to name only a few, have been analyzed from a GameTheoretic perspective. The studied models are simplification of problems arising in real networks, that seem appropriate for describing basic network problems.…”

“…The bounds on the PoA for the aforementioned model were initially analyzed both in pure and mixed strategies setting in [20]. They were later improved by [24], and definitively characterized in [11,21]. The existence of pure Nash equilibrium in this setting was proved in [14].…”

Selección de access point en redes inalámbricas 802.11 garantizando mínima QoS

“…Especí-ficamente, la teoría de juegos ha sido utilizada para analizar topologías de redes [3], [4], enrutamiento de paquetes [5], [6] y [7] y protocolos de transporte [8]. En el área de las comunicaciones inalámbricas, la teoría de juegos se ha utilizado para analizar una gran variedad de problemas entre los cuales se encuentran enrutamiento multisalto [9] y [10], control de potencia [11] y [12], incentivos de participación [13] y valor del acceso inalámbrico [14], [15] y [16].…”

“…De acuerdo a lo anterior, la función de utilidad escogida para dar solución a este juego está determinada por la siguiente ecuación, la cual cumple con el concepto de convexidad y continuidad de acuerdo a [5].…”

On Equilibria for ADM Minimization Games

“…The application of concepts and techniques borrowed from game theory to various problems in computer science, and specifically, to network problems, was initiated in [17,22]. Since then, issues like routing [6,19,24], bandwidth allocation [27], and congestion control [16], to name only a few, have been analyzed from a game theoretic perspective. Typically the studies focus on the worst equilibrium of a given model (that is, on the price of anarchy), since the price of stability often turns out to be 1, yet systems may converge to any possible equilibrium.…”