Social optimality and cooperation in nonatomic congestion games

Abstract

Congestion externalities may result in non-optimal equilibria. For these to occur, it suffices that facilities differ in their fixed utilities or costs. As this paper shows, the only case in which equilibria are always socially optimal, regardless of the fixed components, in that in which the costs increase logarithmically with the size of the set of users. Therefore, achieving a socially optimal choice of facilities generally requires some form of external intervention or cooperation. For heterogeneous populations (in which the fixed utilities or costs vary across users as well as across facilities), this raises the question of utility or cost sharing. The sharing rule proposed in this paper is the Harsanyi transferable-utility value of the game-which is based on the users' marginal contributions to the bargaining power A. Neyman for suggesting the idea of investigating the value of such games. I also thank an anonymous referee and an associate editor for useful comments. several, or many, independent decision-makers interact by using the same facilities. In the nonatomic congestion games studied in this paper, each player only chooses one action or facility, and his utility strictly decreases as the size of the set of other players choosing the same action or facility increases. Different players do not necessarily achieve the same utility when making the same choice. In this respect, the population of players is heterogeneous. However, the manner in which utility decreases with increased congestion is the same for all. The following example (adapted from [4]) illustrates these assumptions. People in a professional meeting may prefer to go to different sessions, since the intrinsic quality they assign to each session varies. As more people crowd into a room, it becomes more difficult to see and hear. The actual quality each person assigns to a session therefore depends on both the intrinsic quality and the number of other people present. The delays experienced by clients in a computer network when many of them simultaneously try to access the same server are another example.In nonatomic congestion games of the kind considered here, the equilibrium payoffs are always unique. Moreover, the equilibria are Pareto efficient in the sense that it is not possible to modify an equilibrium in such a way that some players become better off without making some of the others worse off. However, the equilibria need not be socially optimal. That is, they may all be inferior to some non-equilibrium assignment of facilities in terms of the aggregate, or equivalently average, utility or cost. (Note that, unlike Pareto efficiency, the notion of social optimality involves interpersonal comparisons of utilities.) For the equilibria to maximize social welfare, a player's utility from choosing a facility should reflect the external effects of his choice on the other players. In other words, the cost or benefit for the individual must mirror the social cost or benefit. The first main result of this paper is that, under the assumption...

Comparative statics of altruism and spite

“…For population games, Corollary 2 generalizes a well-known result pertaining to nonatomic congestion games (Milchtaich, 2004).…”

Truthful Mechanisms for Selfish Routing and Two-Parameter Agents

“…We study nonatomic congestion games, in which infinitely many players interact and each player has a negligible ability to affect the others. Nonatomic congestion games have recently been studied in [28][29][30][31]. They are a subclass of the class of nonatomic games introduced by Schmeidler [32].…”

Joint Strategy Fictitious Play with Inertia for Potential Games

“…Any congestion game with utility functions as in (8) is a potential game [6]. 8 A congestion game can be generalized further by allowing player utilities to include player specific attributes [31]. For example, each player may have a personal preference over resources, in which case player utilities take the form where is the fixed utility player receives for using resource .…”

“…For example, each player may have a personal preference over resources, in which case player utilities take the form where is the fixed utility player receives for using resource . Congestion games of this form are also potential games [31].…”

“…The approach is similar to the taxation approaches for nonatomic congestion games proposed in [31], [34].…”