Quitting games – An example

Eilon Solan (1) , Nicolas Vieille (2)

1 TAU - Tel Aviv University
2 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC

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 r S i, 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.

Keywords: cyclic equilibrium; stochastic games; games of timing

Domains: Economy and decision science

Eilon Solan, Nicolas Vieille. Quitting games – An example. International Journal of Game Theory, 2003, Vol.31,n°3, pp.365-381. ⟨10.1007/s001820200125⟩. ⟨hal-00464962⟩