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A class of noncooperative games in which the players share a common set of strategies is described. The payoff a player receives for playing a particular strategy depends only on the total number of players playing the same strategy and decreases with that number in a manner which is specific to the particular player. It is shown that each game in this… (More)

- Igal Milchtaich
- Math. Oper. Res.
- 2005

Equilibrium ‡ow in a physical network with a large number of users (e.g., transportation, communication and computer networks) need not be unique if the costs of the network elements are not the same for all users. Such di¤erences among users may arise if they are not equally a¤ected by congestion or have di¤erent intrinsic preferences. Whether or not, for… (More)

- Igal Milchtaich
- Games and Economic Behavior
- 2006

Different kinds of networks, such as transportation, communication, computer, and supply networks, are susceptible to similar kinds of inefficiencies. These arise when congestion externalities make each user's cost depend on the other users' choices of routes. If each user chooses the least expensive (e.g., fastest) route from the users' common point of… (More)

- Igal Milchtaich
- Math. Oper. Res.
- 2000

A crowding game is a noncooperative game in which the payo¤ of each player depends only on the player's action and the size of the set of players choosing that particular action: The larger the set, the smaller the payo¤. Finite, n-player crowding games often have multiple equilibria. However, a large crowding game generically has just one equilibrium, and… (More)

- Igal Milchtaich
- J. Economic Theory
- 2004

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.… (More)

- Igal Milchtaich
- Games and Economic Behavior
- 2009

Players in a congestion game may differ from one another in their intrinsic preferences (e.g., the benefit they get from using a specific resource), their contribution to congestion, or both. In many cases of interest, intrinsic preferences and the negative effect of congestion are (additively or multiplicatively) separable. This paper considers the… (More)

- Igal Milchtaich
- 1995

The definition of vector measure game is generalized in this paper to include all cooperative games of the form f (, where is a nonatomic vector measure of bounded variation that takes values in a Banach space. It is shown that if f is weakly continuously differentiable on the closed convex hull of the range of then the vector measure game f ( is in… (More)

We consider a special case of weighted congestion games with player-specific latency functions where each player uses for each particular resource a fixed (non-decreasing) delay function together with a player-specific constant. For each particular resource, the resource-specific delay function and the player-specific constant (for that resource) are… (More)

- Igal Milchtaich
- WINE
- 2006

An open problem is presented regarding the existence of pure strategy Nash equilibrium (PNE) in network congestion games with a finite number of non-identical players, in which the strategy set of each player is the collection of all paths in a given network that link the player's origin and destination verti-ces, and congestion increases the costs of… (More)

- Igal Milchtaich, Eyal Winter
- Games and Economic Behavior
- 2002

This paper presents a model of group formation based on the assumption that individuals prefer to associate with people similar to them. It is shown that, in general, if the number of groups that can be formed is bounded, then a stable partition of the society into groups may not exist. (A partition is defined as stable if none of the individuals would… (More)