Eilon Solan and Nicolas Vieille
Mathematics of Operations Research 26 (2001), 265-285.
Quitting games are multi-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 riS, 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 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 with multi-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.