When do market games have transferable utility?
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.
scientific article; zbMATH DE number 3939141
scientific article