Characterizing Existence of Equilibrium for Large Extensive Form Games: A Necessity Result

Klaus Ritzberger; Carlos Alos-Ferrer

doi:10.1007/s00199-015-0937-0

Characterizing Existence of Equilibrium for Large Extensive Form Games: A Necessity Result

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Abstract

What is the minimal structure that is needed to perform equilibrium analysis in large extensive form games? To answer this question, this paper provides conditions that are simultaneously necessary and sufficient for the existence of a subgame perfect equilibrium in any well-behaved perfect information game defined on a large game tree. In particular, the set of plays needs to be endowed with a topology satisfying two conditions. (a) Nodes are closed as sets of plays; and (b) the immediate predecessor function is an open map.

Original language	English
Pages (from-to)	1-24
Number of pages	24
Journal	Economic Theory
DOIs	https://doi.org/10.1007/s00199-015-0937-0
Publication status	Published - 7 Dec 2015

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10.1007/s00199-015-0937-0

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abstract = "What is the minimal structure that is needed to perform equilibrium analysis in large extensive form games? To answer this question, this paper provides conditions that are simultaneously necessary and sufficient for the existence of a subgame perfect equilibrium in any well-behaved perfect information game defined on a large game tree. In particular, the set of plays needs to be endowed with a topology satisfying two conditions. (a) Nodes are closed as sets of plays; and (b) the immediate predecessor function is an open map.",

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