Quitting Games and Linear Complementarity Problems

We prove that every multiplayer quitting game admits a sunspot ε-equilibrium for every ε>0, that is, an ε-equilibrium in an extended game in which the players observe a public signal at every stage. We also prove that, if a certain matrix that is derived from the payoffs in the game is not a Q-matrix in the sense of linear complementarity problems, then the game admits a uniform ε-equilibrium for every ε>0.