Crowding Games are Sequentially Solvable
International Journal of Game Theory 27 (1998), 501–509
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.
Crowding games; Congestion games; Sequential solvability; Pure-strategy equilibria