Non-additive beliefs and strategic equilibria
type: Item
instance of: scholarly article
title: Non-additive beliefs and strategic equilibria
zbMATH Open document ID: 0962.91002
author: Jürgen Eichberger
author: D. Kelsey
published in: Games and Economic Behavior
publication date: 2001-06-11T00:00:00Z
review text: The authors introduce a notion of equilibrium under uncertainty for \(n\)-player games generalizing the notion for \(2\)-player games introduced by \textit{J. Dow} and \textit{S. Ribeiro da Costa Werlang} [J. Econ. Theory 64, 305-324 (1994; Zbl 0813.90132)]. In this framework, beliefs are modelled by (non-additive) capacities. For a capacity \(\nu\), we have two notions measuring the degree of uncertainty: The degree of confidence and the degree of ambiguity. The authors show some facts about their notion: (a) mixed-strategy Nash equilibria are equilibria under uncertainty, (b) pure-strategy maximin strategy combinations are equilibria under uncertainty, (c) if the degree of confidence is sufficiently small, then an equilibrium under uncertainty induces maximin play, and (d) if the beliefs of all players are independent and consistent, then every sequence of equilibria under uncertainty whose degrees of ambiguity converge to zero converges to a Nash equilibrium.
reviewed by: Benedikt Löwe
Mathematics Subject Classification ID: 91A06
Mathematics Subject Classification ID: 91A10
Mathematics Subject Classification ID: 28A12
zbMATH DE Number: 1437104
zbMATH Keywords: non-additive probability
zbMATH Keywords: capacity
zbMATH Keywords: uncertainty
zbMATH Keywords: ambiguity
zbMATH Keywords: confidence
zbMATH Keywords: equilibrium
Wikidata QID: Q57918046
MaRDI profile type: Publication
full work available at URL: game.1998.0724
OpenAlex ID: W2087821684
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DBLP publication ID: journals/geb/EichbergerK00
DOI: 10.1006/GAME.1998.0724
description: scientific article; zbMATH DE number 1437104