Crowding Games are Sequentially Solvable

Posted: 13 Jan 1999

See all articles by Igal Milchtaich

Igal Milchtaich

Bar-Ilan University - Department of Economics

Abstract

A sequential-move version of a given normal-form game [Gamma] is an extensive-form game of perfect information in which each player chooses his action after observing the actions of all players who precede him and the payoffs are determined according to the payoff functions in [Gamma]. A normal-form game [Gamma] is sequentially solvable if each of its sequential-move versions has a subgame-perfect equilibrium in pure strategies such that the players' actions on the equilibrium path constitute an equilibrium of [Gamma].

A crowding game is a normal-form game in which the players share a common set of actions and the payoff a particular player receives for choosing a particular action is a nonincreasing function of the total number of players choosing that action. It is shown that every crowding game is sequentially solvable. However, not every pure-strategy equilibrium of a crowding game can be obtained in the manner described above. A sufficient, but not necessary, condition for the existence of a sequential-move version of the game that yields a given equilibrium is that there is no other equilibrium that Pareto dominates it.

JEL Classification: C70

Suggested Citation

Milchtaich, Igal, Crowding Games are Sequentially Solvable. International Journal of Game Theory, Vol. 27, Iss. 4, December 16, 1998, Available at SSRN: https://ssrn.com/abstract=143206

Igal Milchtaich (Contact Author)

Bar-Ilan University - Department of Economics ( email )

Ramat-Gan, 52900
Israel

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