Crowding games are sequentially solvable |
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Authors: | Igal Milchtaich |
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Institution: | (1) Department of Mathematics and Center for Rationality and Interactive Decision Theory, Hebrew University of Jerusalem, Israel (e-mail: igal@math.huji.ac.il), IL |
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Abstract: | A sequential-move version of a given normal-form game Γ 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 Γ. A normal-form game Γ 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 Γ.
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.
Received July 1997/Final version May 1998 |
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Keywords: | : Crowding games congestion games sequential solvability pure-strategy equilibria |
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