A formula for Nash equilibria in monotone singleton congestion games (original) (raw)

Nash equilibria in singleton congestion games : Symmetric case

2010

This paper provides a simple formula describing all Nash equilibria in singleton congestion games, reducing the complexity of computing all these equilibria and giving a simple and short proof (without invoking the FIP or the potential function).

Nonsymmetric singleton congestion games: case of two resources

2011

In this note we study the existence of Nash equilibria in nonsymmetric finite congestion games, complementing the results obtained by Milchtaich on monotone-decreasing congestion games. More specifically, we examine the case of two resources and we propose a simple method describing all Nash equilibria in this kind of congestion games. Additionally, we give a new and short proof establishing the existence of a Nash equilibrium in this type of games without invoking the potential function or the finite improvement property. (H. Smaoui), abderrahmane.ziad@unicaen.fr (A.Ziad). Example 2 . Let N = {1, 2, 3, 4, 5} and R = {a, b}. Suppose that the players' preferences are given by the following weak ordering:

On the inefficiency of equilibria in congestion games

2005

We present a short geometric proof of the price of anarchy and price of stability results that have recently been established in a series of papers on selfish routing. This novel proof also facilitates two types of new results: On the one hand, we give pseudoapproximation results that depend on the class of allowable cost functions. On the other hand, we offer improved bounds on the inefficiency of Nash equilibria for situations in which the equilibrium travel times are within reasonable limits of the free-flow travel times, a scenario that captures empirical observations in vehicular traffic networks. Our results actually hold in the more general context of congestion games, which provide the framework in which we describe this work.

Congestion Games and Potentials Reconsidered

International Game Theory Review, 1999

In congestion games, players use facilities from a common pool. The benefit that a player derives from using a facility depends, possibly among other things, on the number of users of this facility. The paper gives an easy alternative proof of the isomorphism between exact potential games and the set of congestion games introduced by Rosenthal (1973). It clarifies the relations between existing models on congestion games, and studies a class of congestion games where the sets of Nash equilibria, strong Nash equilibria and potential-maximising strategies coincide. Particular emphasis is on the computation of potential-maximising strategies.

Nash equilibria in nonsymmetric singleton congestion games with exact partition

2011

We define a new class of games, which we qualify as congestion games with exact partition. These games constitute a subfamily of singleton congestion games for which the players are restricted to choose only one strategy, but they each possess their own utility function. The aim of this paper is to develop a method leading to an easier identification of

Solution-based congestion games

In this paper we develop the theory of potential of cooperative games for semivalues, characterize congestion models that are defined by semivalues, and suggest an application of these results to combinatorial auctions, which may explain the success of the Iowa electronic market. and they have been analyzed by several researchers from various additional fields, in particular computer science 2 , communication networks 3 , and economics/game theory. 4

On Singleton Congestion Games with Resilience Against Collusion

Lecture Notes in Computer Science, 2021

We study the subclass of singleton congestion games with identical and increasing cost functions, i.e., each agent tries to utilize from the least crowded resource in her accessible subset of resources. Our main contribution is a novel approach for proving the existence of equilibrium outcomes that are resilient to weakly improving deviations: (i) by singletons (Nash equilibria), (ii) by the grand coalition (Pareto efficiency), and (iii) by coalitions with respect to an a priori given partition coalition structure (partition equilibria). To the best of our knowledge, this is the strongest existence guarantee in the literature of congestion games that is resilient to weakly improving deviations by coalitions.

Bounding the inefficiency of equilibria in nonatomic congestion games

Games and Economic Behavior, 2004

Equilibria in noncooperative games are typically inefficient, as illustrated by the Prisoner's Dilemma. In this paper, we quantify this inefficiency by comparing the payoffs of equilibria to the payoffs of a "best possible" outcome. We study a nonatomic version of the congestion games defined by Rosenthal , and identify games in which equilibria are approximately optimal in the sense that no other outcome achieves a significantly larger total payoff to the players-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 games . * We thank Lou Billera for encouraging us to explore generalizations of our previous work on traffic routing, and Robert Rosenthal for introducing us to his congestion games. The first author thanks Amir Ronen for comments on a previous paper [16] that facilitated a generalization of the results therein to the nonatomic congestion games of this paper.

On the Inefficiency Ratio of Stable Equilibria in Congestion Games

Lecture Notes in Computer Science, 2009

Price of anarchy and price of stability are the primary notions for measuring the efficiency (i.e. the social welfare) of the outcome of a game. Both of these notions focus on extreme cases: one is defined as the inefficiency ratio of the worst-case equilibrium and the other as the best one. Therefore, studying these notions often results in discovering equilibria that are not necessarily the most likely outcomes of the dynamics of selfish and non-coordinating agents. The current paper studies the inefficiency of the equilibria that are most stable in the presence of noise. In particular, we study two variations of non-cooperative games: atomic congestion games and selfish load balancing. The noisy best-response dynamics in these games keeps the joint action profile around a particular set of equilibria that minimize the potential function. The inefficiency ratio in the neighborhood of these "stable" equilibria is much better than the price of anarchy. Furthermore, the dynamics reaches these equilibria in polynomial time. Our observations show that in the game environments where a small noise is present, the system as a whole works better than what a pessimist may predict. They also suggest that in congestion games, introducing a small noise in the payoff of the agents may improve the social welfare.

On the Performance of Approximate Equilibria in Congestion Games

Algorithmica, 2011

We study the performance of approximate Nash equilibria for congestion games with polynomial latency functions. We consider how much the price of anarchy worsens and how much the price of stability improves as a function of the approximation factor ε. We give tight bounds for the price of anarchy of atomic and non-atomic congestion games and for the price of