Quitting Games

Quitting games aren-player sequential games in which, at any stage, each player has the choice betweencontinuing andquitting. The game ends as soon asat least one player chooses to quit; playeri then receives a payoffr iS , which depends on the setS of players that did choose to quit. If the game never ends, the payoff to each player is 0.The paper has four goals: (i) We prove the existence of a subgame-perfect uniform e-equilibrium under some assumptions on the payoff structure; (ii) we study the structure of the e-equilibrium strategies; (iii) we present a new method for dealing withn-player games; and (iv) we study an example of a four-player quitting game where the "simplest" equilibrium is cyclic with Period 2.We also discuss the relation to Dynkin's stopping games and provide a generalization of our result to these games.

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