Sunspot equilibrium in positive recursive general quitting games

We prove that positive recursive general quitting games, which are quitting games in which (a) each player has a single quitting action and possibly several continue actions, (b) the stage payoff as long as quitting does not occur is 0, and (c) the payoff when quitting occurs is non-negative, admit a sunspot $$\varepsilon $$ -equilibrium, for every $$\varepsilon > 0$$ .