Quitting Games - an Example
Eilon Solan and Nicolas Vieille
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 zero.
We exhibit a four-player quitting game, where any e-equilibrium involves some kind of cyclic behavior, in which the probability of quitting in any stage is bounded away from zero. We argue that all known method to prove existence of an equilibrium payoff in multi-player stochastic games are therefore bound to fail, and provide some geometric intuition for this phenomenon.