Quitting Games and Linear Complementarity Problems

TL;DR

This paper establishes the existence of approximate equilibria in multiplayer quitting games, linking game theory with linear complementarity problems through the concept of Q-matrices.

Contribution

It proves that all multiplayer quitting games have approximate sunspot equilibria and connects the existence of Nash equilibria to the Q-matrix condition in linear complementarity problems.

Findings

Existence of sunspot ε-equilibria in multiplayer quitting games.

Connection between game equilibria and linear complementarity problem matrices.

Identification of Q-matrix conditions ensuring Nash ε-equilibria.

Abstract

We prove that every multiplayer quitting game admits a sunspot $\varepsilon$-equilibrium for every $\varepsilon > 0$, that is, an $\varepsilon$-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 $\varepsilon$-equilibrium for every $\varepsilon > 0$.