Robert Samuel Simon
Escape Games
Preprint series: Mathematica Gottingensis
90D15 Stochastic games, See also {93E05}
Abstract: We prove the existence of approximate equilibria for a special class of
quitting games called ``escape games''.
A quitting game is an
game played on an infinitely many stages with finitely many players $N$
where every player in $N$
has only two moves, ``q'' to end the game with certainty
or ``c'' to allow the game
to continue to the next stage.
If nobody ever acts to end the game, all players receive
payoffs of $0$.
The importance of quitting games is that they are the simplest form
of stochastic games for which the existence of approximate
equilibria is in doubt. The proof for escape games reveals
much about quitting games and their approximate equilibria, indeed
about stochastic games in general.
The most important technique of the proof belongs to algebraic topology.

Keywords: Stochastic Games, Dynamic Systems (Discrete Time)