Preface - 6[-]Contents - 8[-]List of Figures - 10[-]List of Tables - 12[-]List of Algorithms - 14[-]1 Introduction - 16[-]2 Stochastic Games - 32[-]3 Equilibria - 56[-]4 Complexity of Equilibria - 78[-]5 Decidable Fragments - 100[-]6 Conclusion - 136[-]Appendix A Preliminaries - 142[-]Appendix B Markov Chains and Markov Decision Processes - 150[-]Bibliography - 158[-]Notation - 170[-]Index - 172Stochastic games provide a versatile model for reactive systems that are affected by random events. This dissertation advances the algorithmic theory of stochastic games to incorporate multiple players, whose objectives are not necessarily conflicting. The basis of this work is a comprehensive complexity theoretic analysis of the standard game-theoretic solution concepts in the context of stochastic games over a finite state space. One main result is that the constrained existence of a Nash equilibrium becomes undecidable in this setting. This impossibility result is accompanied by several positive results, including efficient algorithms for natural special cases.

Michael Ummels received his diploma degree in computer science from RWTH Aachen University. He started his doctoral studies at the same university in 2006, supervise by Prof. Dr. Erich Grädel and Prof. Dr. Dr.h.c. Wolfgang Thomas. As ofFebruary 2010, the author is a postdoctoral researcher at ENS Cachan.