On comparing equilibrium and optimum payoffs in a class of discrete bimatrix games
type: Item
instance of: scholarly article
title: On comparing equilibrium and optimum payoffs in a class of discrete bimatrix games
zbMATH Open document ID: 0941.91004
DOI: 10.1016/S0165-4896(99)00005-0
published in: Mathematical Social Sciences
publication date: 2000-08-02T00:00:00Z
review text: Each \(m_1\times m_2\) payoff matrix in the bimatrix games studied here is formed by a random permutation of the integers from 1 to \(M=m_1m_2\). The author is interested in comparing a ``random pure strategy Nash equilibrium payoff'' with a ``random pure Pareto optimal outcome payoff'', in a certain sense of those terms, ignoring the possibility of mixed strategies. The payoff numbers are regarded as simply giving ordinal rankings of the outcomes, and except in the \(2\times 2\) case another restriction is made in order to get a dominance relation between the two above-mentioned types of random payoff: that the players have concave von Neumann-Morgenstern utility functions over ordinally ranked pure outcomes. The main theorem states that in this case, if \(m_1>2\sum_{n=1}^{M}{1\over n}\) then expected payoff for a random (in the sense considered) pure strategy Nash equilibrium dominates that for a random pure Pareto optimal outcome. In particular the conclusion is valid when \(m_1=m_2\) or \(m_1\geq m_2\geq 9\). (When \(m_1=m_2 \geq 9\) the inequality of the main theorem holds; if \(m_1=m_2<9\), an alternate more complicated sufficient condition is satisfied).
reviewed by: Gerald A. Heuer
Mathematics Subject Classification ID: 91A05
Mathematics Subject Classification ID: 91A10
zbMATH DE Number: 1406426
zbMATH Keywords: bimatrix games
zbMATH Keywords: equilibrium
zbMATH Keywords: optimum payoffs
author: William G. Stanford
MaRDI profile type: Publication
cites work: Stochastic Dominance on Unidimensional Grids
cites work: The Efficiency Analysis of Choices Involving Risk
cites work: The Number of Outcomes in the Pareto-Optimal Set of Discrete Bargaining Games
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description: scientific article; zbMATH DE number 1406426