Characterizations of the equilibrium payoffs of inertia supergames
type: Item
instance of: scholarly article
title: Characterizations of the equilibrium payoffs of inertia supergames
zbMATH Open document ID: 0705.90105
DOI: 10.1016/0022-0531(90)90056-P
author: Subir K. Chakrabarti
published in: Journal of Economic Theory
publication date: 1990-01-01T00:00:00Z
review text: An inertia supergame is one in which changing strategies over time is not merely costly, but the cost incurred by any player in changing strategies is greater than any gains made in a single period. Define \(V^*\), a payoff vector in the convex hull of the set of payoff vectors of the one- shot game, to be an I-sustainable payoff if for all \(i\in N\) and \(x^ i_{\ell}\in X^ i\) there exists \(x_{\ell}^{N\setminus \{i\}}\in N^{N\setminus \{i\}}\) such that for any finite index set L, \[ \sum_{\ell \in L}p(\ell)U^ i(x^ i_{\ell},x_{\ell}^{N\setminus \{i\}})\leq v^ i_*. \] Note: Here \(\Delta (L)=\{p: L\to (0,1]| \sum_{\ell \in L}p(\ell)=1\}\), where L is a finite index set. We show that the set of payoff vectors of the strong, perfect equilibrium points of the inertia supergame are exactly the I-sustainable payoffs of the one-shot game. We also find that if one allows for a correlating device that induces the Borel sigma algebra on the strategy space of the one-shot game, then the correlated \(\alpha\)-core is the topological closure of the set of payoffs of the strong, perfect equilibrium points of the inertia supergame.
reviewed by: Subir K. Chakrabarti
Mathematics Subject Classification ID: 91A20
zbMATH DE Number: 4158424
zbMATH Keywords: inertia supergame
zbMATH Keywords: I-sustainable payoff
zbMATH Keywords: strong, perfect equilibrium points
zbMATH Keywords: one-shot game
zbMATH Keywords: correlated \(\alpha \) -core
MaRDI profile type: Publication
cites work: Acceptable points in games of perfect information
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description: scientific article; zbMATH DE number 4158424