On games and equilibria with coherent lower expectations
type: Item
instance of: scholarly article
title: On games and equilibria with coherent lower expectations
zbMATH Open document ID: 1394.91017
DOI: 10.1155/2015/690295
author: Giuseppe De Marco
author: Maria Romaniello
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: Different solution concepts for strategic form games have been introduced in order to weaken the consistency assumption that players' beliefs, about their opponents strategic choices, are correct in equilibrium. The literature has shown that ambiguous beliefs are an appropriate device to deal with this task. In this note, we introduce an equilibrium concept in which players do not know the opponents' strategies in their entirety but only the \textit{coherent lower expectations} of some random variables that depend on the actual strategies taken by the others. This equilibrium concept generalizes the already existing concept of equilibrium with partially specified probabilities by extending the set of feasible beliefs and allowing for comparative probability judgements. We study the issue of the existence of the equilibrium points in our framework and find sufficient conditions which involve the continuity of coherent lower expectations and a Slater-like condition for the systems of inequalities defining beliefs.
Mathematics Subject Classification ID: 91A10
Mathematics Subject Classification ID: 91A26
zbMATH DE Number: 6926996
Wikidata QID: Q59118938
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/690295
OpenAlex ID: W1536686398
cites work: Random belief equilibrium in normal form games
cites work: Nash equilibrium under Knightian uncertainty: Breaking down backward induction
cites work: Non-additive beliefs and strategic equilibria
cites work: Ambiguous games
cites work: Equilibrium in beliefs under uncertainty
cites work: Nash equilibrium with lower probabilities
cites work: Variational preferences and equilibria in games under ambiguous belief correspondences
cites work: Towards a unified theory of imprecise probability
cites work: Set-valued analysis
cites work: Stability Theory for Systems of Inequalities. Part I: Linear Systems
cites work: A limit theorem for equilibria under ambiguous belief correspondences
cites work: Remarks on Perturbations in Linear Inequalities
description: scientific article; zbMATH DE number 6926996