Sunspot Equilibrium in General Quitting Games

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.