The Theory of Extensive Form Games

Nonfiction, Science & Nature, Mathematics, Game Theory, Business & Finance, Economics, Theory of Economics
Cover of the book The Theory of Extensive Form Games by Klaus Ritzberger, Carlos Alós-Ferrer, Springer Berlin Heidelberg
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Author: Klaus Ritzberger, Carlos Alós-Ferrer ISBN: 9783662499443
Publisher: Springer Berlin Heidelberg Publication: July 8, 2016
Imprint: Springer Language: English
Author: Klaus Ritzberger, Carlos Alós-Ferrer
ISBN: 9783662499443
Publisher: Springer Berlin Heidelberg
Publication: July 8, 2016
Imprint: Springer
Language: English

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.

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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.

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