Quitting Games

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 rⁱ_S, 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.