A Course in Stochastic Game Theory

This book presents a course on stochastic games and the mathematical methods used in their analysis. Assuming only basic undergraduate mathematics, it includes numerous examples and exercises, with solutions available online, making it suitable for beginning graduate students and newcomers from other areas of mathematics and 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.