Equilibrium

Carlos Alós-Ferrer and Klaus Ritzberger

Chapter 7 in The Theory of Extensive Form Games, 2016, pp 163-222 from Springer

Abstract: Abstract This chapter takes advantage of the findings in previous chapters and tackles a first problem in solution theory: Given a discrete game tree, what are the properties of a topology on the set of plays which guarantee that every perfect information game defined on this tree has a subgame perfect equilibrium, as long as the players’ preferences are continuous and decision points are suitably assigned? The main result of this chapter is a characterization: In such a (compact and perfectly normal) topology all nodes must be closed and the immediate predecessor function must map open sets to open sets. The necessity part of this characterization holds without compactness, the sufficiency part with a weaker separation axiom. Hence, ultimately the approach of this manuscript leads to the most general existence theorem for perfect information games.

Keywords: Nash Equilibrium; Perfect Information; Subgame Perfect Equilibrium; Game Tree; Close Node (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spschp:978-3-662-49944-3_7

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DOI: 10.1007/978-3-662-49944-3_7

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