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Stochastic games are 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.

In developing countries with weak institutions, there is implicitly a large reliance on elections to instill norms of accountability and reduce corruption. In this paper we show that electoral discipline may be ineffective in reducing corruption when political competition is too high or too low. We first build a simple game theoretic model to capture the effect of electoral competition on corruption. We show that in equilibrium, corruption has a U-shaped relationship with electoral competition. If the election is safe for the incumbent (low competition) or if it is extremely fragile (high competition) then corruption is higher, and for intermediate levels of competition, corruption is lower. We also predict that when there are different types of corruption, then incumbents increase corruption in the components that voters care less about regardless of competition. We test the model's predictions using data gathered on audit findings of leakages from a large public program in Indian villages belonging to the state of Andhra Pradesh during 2006-10 and on elections to the village council headship in 2006. Our results largely confirm the theoretical results that competition has a non-linear effect on corruption, and that the impact of electoral competition varies by whether theft is from the public or private component of the service delivery. Overall, our results suggest that over-reliance on elections to discipline politicians is misplaced.

"Covering both noncooperative and cooperative games, this comprehensive introduction to game theory also includes some advanced chapters on auctions, games with incomplete information, games with vector payoffs, stable matchings, and the bargaining set. Mathematically oriented, the book presents every theorem alongside a proof. The material is presented clearly and every concept is illustrated with concrete examples from a broad range of disciplines. With numerous exercises the book is a thorough and extensive guide to game theory from undergraduate through graduate courses in economics, mathematics, computer science, engineering, and life sciences to being an authoritative reference for researchers"--