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.