Quitting games

Quitting games are n-player sequential games in which, at any stage, each player has the choice between continuing and quitting. The game ends as soon as at least one player chooses to quit; player i then receives a payoff r_sⁱ, which depends on the set S 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 ε-equilibrium under some assumptions on the payoff structure; (ii) we study the structure of the ε-equilibrium strategies; (iii) we present a new method for dealing with n-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.