Sunspot Equilibrium in General Quitting Games

Abstract

We prove that positive recursive general quitting games, which are quitting games in which each player may have more than one continue action, admit a sunspot $\ep$-equilibrium, for every $\ep > 0$. To this end we show that the equilibrium set of strategic-form games can be uniformly approximated by a smooth manifold, and develop a new fixed-point theorem for smooth manifolds.