The
Dynamics of the Nash Correspondence and $n$-Player Stochastic Games

Eilon
Solan

International
Game Theory Review 3 (2001),
291-300.

A *quitting game* is a sequential
game where each player has two actions: to *continue* or to *quit*,
and the game continues as long as no player quits.

We study an example of a three player
quitting game that admits a uniform equilibrium payoff,
and show that the correspondence
that assigns to every continuation
payoff the set of Nash equilibria in the corresponding one shot game does not
admit non trivial periodic points.

The study presented here has an implication on the approach one should
take in trying to prove, or disprove, the existence of an equilibrium payoff in multi-player stochastic
games. It also shows that the minimal length of the period of a periodic e-equilibrium in three-player quitting
games needs not be uniformly bounded for e > 0.