Game Theory

This book is a formalization of collected notes from an introductory game theory course taught at Queen's University. The course introduced traditional game theory and its formal analysis, but also moved to more modern approaches to game theory, providing a broad introduction to the current state of the discipline. Classical games, like the Prisoner's Dilemma and the Lady and the Tiger, are joined by a procedure for transforming mathematical games into card games. Included is an introduction and brief investigation into mathematical games, including combinatorial games such as Nim. The text examines techniques for creating tournaments, of the sort used in sports, and demonstrates how to obtain tournaments that are as fair as possible with regards to playing on courts. The tournaments are tested as in-class learning events, providing a novel curriculum item. Example tournaments are provided at the end of the book for instructors interested in running a tournament in their own classroom.The book is appropriate as a text or companion text for a one-semester course introducing the theory of games or for students who wish to get a sense of the scope and techniques of the field.

Auteur

Andrew McEachern obtained his Ph.D. in Applied Mathematics in 2013 from the University of Guelph, in Ontario, Canada. He is a Coleman postdoctoral Fellow at Queens University, and his research interests include evolutionary computation, applied game theory, mathematics education initiatives, and mathematics curriculum development for elementary and high school students.

Contenu
Preface.- Acknowledgments.- Introduction: The Prisoner's Dilemma and Finite State Automata.- Games in Extensive Form with Complete Information and Backward Induction.- Games in Normal Form and the Nash Equilibrium.- Mixed Strategy Nash Equilibria and Two-Player Zero-Sum Games.- Mathematical Games.- Tournaments and Their Design.- Afterword.- Bibliography.- Author's Biography.