Logic in Games

This book, published by the MIT Press in 2014, draws on ideas from philosophical logic, computational logic, multiagent systems, and game theory to offer a comprehensive account of the interface of logic and games viewed in two complementary directions. It examines the logic of games: the development of logical systems that analyze the interactive strategic structure of games, the role of preferences over outcomes, as well as the information flow between players. It also examines the opposite direction of logic as games: where reasoning and related logical tasks are cast in the form of games. The two directions are entangled in various ways, and the book also discusses a number of topics that combine features of both.

The book presents new results on invariances and zoom levels for games, modal logics for strategies, preference, knowledge and belief in games, fixed-point logics for solution procedures and equilibria, and dynamic-epistemic and temporal logics of agency for players. There are also chapters on interactions between games and the foundations of computation, and on logic-driven game design. The book also offers a unifying perspective on a wide range of literature on logic and games over the past 20 years. 

In the course of this, the book takes up the “intelligent interaction" of agents engaging in competitive or cooperative activities and examines the patterns of strategic behavior that arise. It employs dynamic-epistemic logics that analyze information-driven changes in players’ knowledge and beliefs, and introduces the “Theory of Play" that emerges from the combination of logic and game theory. This results in a new view of logic itself as an interactive rational activity based on reasoning, perception, and communication.