Game Trees

Carlos Alós-Ferrer and Klaus Ritzberger

Chapter 2 in The Theory of Extensive Form Games, 2016, pp 17-55 from Springer

Abstract: Abstract This chapter focuses on the representation of the objective description of the game—the game tree. It explores the connections between trees as partially ordered sets, like graphs, and trees as collections of subsets of an underlying set of plays or outcomes. In particular, it identifies a canonical set representation for every tree. This leads to the concept of a game tree: A collection of nonempty subsets of the set of plays that satisfies Trivial Intersection, Boundedness, and Irreducibility. The main theorem of this chapter demonstrates that a game tree preserves the freedom to start from plays or nodes as primitives, hence simultaneously generalizing the approaches of Kuhn and von Neumann and Morgenstern.

Date: 2016
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DOI: 10.1007/978-3-662-49944-3_2

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