Equilibrium states of random economies with locally interacting agents and solutions to stochastic variational inequalities in (L1, L∞)

Equilibrium states of random economies with locally interacting agents and solutions to stochastic variational inequalities in (L1, L∞)

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Article ID: iaor20031433
Country: Netherlands
Volume: 114
Issue: 1
Start Page Number: 145
End Page Number: 165
Publication Date: Aug 2002
Journal: Annals of Operations Research
Authors: ,
Abstract:

We study a stochastic model of an economy with locally interacting agents. The basis of the study is a deterministic model of dynamic economic equilibrium proposed by Polterovich. We generalize Polterovich's theory, in particular, in two respects. We introduce stochastics and consider a version of the model with local interactions between the agents. The structure of the interactions is described in terms of random fields on a directed graph. Equilibrium states of the system are solutions to certain variational inequalities in spaces of random vectors. By analyzing these inequalities, we establish an existence theorem for equilibrium, which generalizes and refines a number of previous results.

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