When do market games have transferable utility?
type: Item
instance of: scholarly article
title: When do market games have transferable utility?
zbMATH Open document ID: 0585.90109
DOI: 10.1016/0022-0531(85)90041-9
author: Theodore C. Bergstrom
author: Hal R. Varian
published in: Journal of Economic Theory
publication date: 1985-01-01T00:00:00Z
full work available at URL: http://hdl.handle.net/2027.42/25608
review text: Several well-known solution concepts of game theory, such as the Shapley value, the kernel and the nucleolus, were, in their original formulations, defined only for games with transferable utility. This is why game theorists like to work with transferable utility. Economists, on the other hand, are uncomfortable with transferable utility because it is not in general possible to model a well-behaved exchange economy as a transferable utility game. The present paper addresses itself to the question of whether there are economically interesting conditions which ensure that market games have transferable utility. It is shown that an exchange economy generates a game with transferable utility if the indirect utility is of the Gorman polar form. This class of utility functions is of the form \(v_ i(p_ im_ i)=\alpha (p)m_ i+\beta_ i(p)\) where \(v_ i\) is consumer i's indirect utility, p is the price vector, and \(m_ i\) is consumer i's income. A converse result is also proven. If there is a transferable utility in a neighbourhood of a Pareto efficient allocation then it must be that in a neighbourhood of the price vector that sustains this allocation as a competitive equilibrium, indirect utility is representable in the Gorman polar form.
Mathematics Subject Classification ID: 91A40
Mathematics Subject Classification ID: 91B24
Mathematics Subject Classification ID: 91B16
Mathematics Subject Classification ID: 91A35
zbMATH DE Number: 3939141
zbMATH Keywords: market games
zbMATH Keywords: transferable utility
zbMATH Keywords: exchange economy
zbMATH Keywords: Gorman polar form
zbMATH Keywords: Pareto efficient allocation
zbMATH Keywords: competitive equilibrium
MaRDI profile type: Publication
OpenAlex ID: W2100658395
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description: scientific article; zbMATH DE number 3939141