The Theory of Extensive Form Games [Hardcover]

This book treats extensive form game theory in full generality. It provides a framework that does not rely on any finiteness assumptions at all, yet covers the finite case. The presentation starts by identifying the appropriate concept of a game tree. This concept represents a synthesis of earlier approaches, including the graph-theoretical and the decision-theoretical ones. It then provides a general model of sequential, interpersonal decision making, called extensive decision problems. Extensive forms are a special case thereof, which is such that all strategy profiles induce outcomes and do so uniquely. Requiring the existence of immediate predecessors yields discrete extensive forms, which are still general enough to cover almost all applications. The treatment culminates in a characterization of the topologies on the plays of the game tree that admit equilibrium analysis.

Introduction.- Game Trees.- Pseudotrees and Order Theory.- Extensive Decision Problems.- Extensive Forms.- Discrete Extensive Forms.- Equilibrium.- A Mathematical Appendix.

This book is written for game theorists interested in the mathematical foundations of their discipline. ... This book provides a useful reference on the ways of analyzing large (infinite) game trees. It will be interesting to see follow-ups by these or other authors, extending this to imperfect information games. It seems that the topology on the space of moves can be related to Borel algebras on information sets, and therefore provide the basis of the probabilistic measures that yield expected payoffs. (Fernando Tohm?, zbMath 1410.91003, 2019)