Quitting Games: An Example

E. Solan, N. VIEILLE

International Journal of Game Theory

2003, vol. 31, n°3, pp.365-381

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)

Quitting games are multi-player sequential games in which, at every stage, each player has the choice between continuing and quitting. The game ends as soon as at least one player chooses to quit; each player i then receives a payoff rSi, which depends on the set S of players that did choose to quit. If the game never ends, the payoff to each player is zero.We exhibit a four-player quitting game, where the "simplest" equilibrium is periodic with period two. We argue that this implies that all known methods to prove existence of an equilibrium payoff in multi-player stochastic games are therefore bound to fail in general, and provide some geometric intuition for this phenomenon.