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Equilibrium States of Random Economies with Locally Interacting Agents and Solutions to Stochastic Variational Inequalities in 〈L 1 ,L ∞ 〉

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  • I.V. Evstigneev
  • M.I. Taksar

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. Copyright Kluwer Academic Publishers 2002

Suggested Citation

  • I.V. Evstigneev & M.I. Taksar, 2002. "Equilibrium States of Random Economies with Locally Interacting Agents and Solutions to Stochastic Variational Inequalities in 〈L 1 ,L ∞ 〉," Annals of Operations Research, Springer, vol. 114(1), pages 145-165, August.
    • Handle: RePEc:spr:annopr:v:114:y:2002:i:1:p:145-165:10.1023/a:1021010220217
    DOI: 10.1023/A:1021010220217
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    Cited by:

    1. Evstigneev, Igor & Taksar, Michael, 2009. "Dynamic interaction models of economic equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 166-182, January.
    2. De Kamps, Marc & Ladley, Daniel & Simaitis, Aistis, 2014. "Heterogeneous beliefs in over-the-counter markets," Journal of Economic Dynamics and Control, Elsevier, vol. 41(C), pages 50-68.
    3. Patrizia Daniele & Sofia Giuffrè, 2015. "Random Variational Inequalities and the Random Traffic Equilibrium Problem," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 363-381, October.
    4. Dan Ladley & Seth Bullock, 2008. "The Strategic Exploitation of Limited Information and Opportunity in Networked Markets," Computational Economics, Springer;Society for Computational Economics, vol. 32(3), pages 295-315, October.

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