TY - JOUR

T1 - Generic uniqueness of equilibrium in large crowding games

AU - Milchtaich, Igal

PY - 2000

Y1 - 2000

N2 - A crowding game is a noncooperative game in which the payoff 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 payoff. Finite, n-player crowding games often have multiple equilibria. However, a large crowding game generically has just one equilibrium, and the equilibrium payoffs in such a game are always unique. Moreover, the sets of equilibria of the m-replicas of a finite crowding game generically converge to a singleton as m tends to infinity. This singleton consists of the unique equilibrium of the `limit' large crowding game. This equilibrium genetically has the following graph-theoretic property: The bipartite graph, in which each player in the original, finite crowding game is joined with all best-response actions for (copies of) that player, does not contain cycles.

AB - A crowding game is a noncooperative game in which the payoff 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 payoff. Finite, n-player crowding games often have multiple equilibria. However, a large crowding game generically has just one equilibrium, and the equilibrium payoffs in such a game are always unique. Moreover, the sets of equilibria of the m-replicas of a finite crowding game generically converge to a singleton as m tends to infinity. This singleton consists of the unique equilibrium of the `limit' large crowding game. This equilibrium genetically has the following graph-theoretic property: The bipartite graph, in which each player in the original, finite crowding game is joined with all best-response actions for (copies of) that player, does not contain cycles.

UR - http://www.scopus.com/inward/record.url?scp=0034245398&partnerID=8YFLogxK

U2 - 10.1287/moor.25.3.349.12220

DO - 10.1287/moor.25.3.349.12220

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AN - SCOPUS:0034245398

SN - 0364-765X

VL - 25

SP - 349

EP - 364

JO - Mathematics of Operations Research

JF - Mathematics of Operations Research

IS - 3

ER -