Solving subclasses of multi-player stochastic games via linear complementarity problem formulations—a survey and some new results

Abstract

We briefly survey some results on the orderfield property of 2-player and multi-player stochastic games and their mixtures. Some of these classes of stochastic games can be solved by formulating them as a Linear Complementarity Problem (LCP) or (Generalized) Vertical Linear Complementarity Problem (VLCP). We discuss some of these results and prove that certain new subclasses and mixtures of multi-player (or n-person) stochastic games can be solved via LCP formulations.