Quitting Games and Linear Complementarity Problems

Abstract

We prove that every multiplayer quitting game admits a sunspot $\epsilon$-equilibrium for every $\epsilon >0$, that is, an $\epsilon$-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 a $Q$-matrix in the sense of linear complementarity problems, then the game admits a Nash $\epsilon$-equilibrium for every $\epsilon >0$.