MeasureBased Values of Market Games
Sergiu Hart
Abstract
The idea of "marginal contribution" is best captured in the game
theoretic concept of value. The relation between it and the usual economic
equilibrium can be stated
as the following Value
Principle: in a perfectly
competitive economy, every value allocation is competitive, and the
two sets of allocations are identical if the
economy is sufficiently differentiable. However, when modelling perfect
competition by a nonatomic space of agents, the (asymptotic)
value may fail to exist in the general
(nondifferentiable) case. The purpose of this paper is to extend
its existence by
addition of a suitable requirement  namely, that it be
"consistent" with the given "population measure." Furthermore,
the competitive price corresponding to the value
allocation  for which we get an explicit formula  has
interesting economic interpretations, as an
"expected equilibrium price," or as an "average best price,"
both corresponding to a random sample
(coalition) of agents.

Mathematics of Operations Research 5 (1980), 2, 197228