A Course in Stochastic Game Theory

Stochastic Games Have An Element Of Chance: The State Of The Next Round Is Determined Probabilistically Depending Upon Players'' Actions And The Current State. Successful Players Need To Balance The Need For Short-Term Payoffs While Ensuring Future Opportunities Remain High. The Various Techniques Needed To Analyze These Often Highly Non-Trivial Games Are A Showcase Of Attractive Mathematics Including Methods From Probability Differential Equations Algebra And Combinatorics. This Book Presents A Course On The Theory Of Stochastic Games Going From The Basics Through To Topics Of Modern Research Focusing On Conceptual Clarity Over Complete Generality. Each Of Its Chapters Introduces A New Mathematical Tool Including Contracting Mappings Semi-Algebraic Sets Infinite Orbits And Ramsey''S Theorem Among Others Before Discussing The Game-Theoretic Results They Can Be Used To Obtain. The Author Assumes No More Than A Basic Undergraduate Curriculum And Illustrates The Theory With Numerous Examples And Exercises With Solutions Available Online.