Measure-Based Values of Market Games

Sergiu Hart


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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.