Theory of Games

Games and elections are fundamental activities in society with applications in economics, political science, and sociology. These topics offer familiar, current, and lively subjects for a course in mathematics.

The English edition differs only slightly from the Russian original. The main struc­ tural difference is that all the material on the theory of finite noncooperative games has been collected in Chapter 2, with renumbering of the material of the remain­ ing chapters. New sections have been added in this chapter: devoted to general questions of equilibrium theory in nondegenerate games, subsections 3.9-3.17, by N.N. Vorob'ev, Jr.; and § 4, by A.G. Chernyakov; and § 5, by N.N. Vorob'ev, Jr., on the computational complexity of the process of finding equilibrium points in finite games. It should also be mentioned that subsections 3.12-3.14 in Chapter 1 were written by E.B. Yanovskaya especially for the Russian edition. The author regrets that the present edition does not reflect the important game-theoretical achievements presented in the splendid monographs by E. van Damme (on the refinement of equilibrium principles for finite games), as well as those by J.e. Harsanyi and R. Selten, and by W. Giith and B. Kalkofen (on equilibrium selection).

The Theory of Search Games and Rendezvous widens the dimensions to the classical problem with the addition of an independent player of equal status to the searcher, who cares about being found or not being found.

This book uses game theory to analyze the strategies developed in negotiation processes. Offering a detailed analysis of competition and cooperation, it explores various bargaining strategies that result from the application of Nash equilibrium and mixed strategies. Employing a blend of game theory and real-world examples, the authors describe typical negotiation scenarios and unveil the art of negotiation strategy – dissecting both competitive and cooperative tactics.

This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions.

This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions.