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A Framework for Studying Economic Interactions (with applications to corruption and business cycles)

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  • Randal J. Verbrugge

    (VPI&SU)

Abstract

Most economic models implicitly or explicitly assume that interactions between economic agents are 'global' - in other words, each agent interacts in a uniform manner with every other agent. However, localized interactions between microeconomic agents are a pervasive feature of reality. What are the implications of more limited interaction? One set of mathematical tools which appears useful in exploring the economic implications of local interactions is the theory of interacting particle systems. Unfortunately, the extant theory mainly addresses the long-time behavior of infinite systems, and focuses on the issue of ergodicity; many economic applications involve a finite number of agents and are concerned with other issues, such as the extent of shock amplification. In this paper, I introduce a framework for studying local interactions that is applicable to a wide class of games. In this framework, agents receive shocks which are stochastically independent; payoffs depend both upon the shocks and the strategies of other agents. In finite games, ergodicity is straightforward to determine. In finite games which evolve in continuous time, the stationary distribution (if it exists) may be computed easily; furthermore, in this class of games, I prove that any stationary distribution may be attained by suitable choice of payoff functions using shocks which are distributed uniform on (0, 1). In systems in which all interactions are global, I prove that nonlinear behavior can arise even in the infinite limit (thus demonstrating that laws of large numbers can fail in systems characterized by interaction), despite the fact that the only driving forces are agent-level iid disturbances. Using numerical methods, I investigate the properties of the processes as one passes from discrete to continuous time, as one alters the pattern of interaction, and as one increases the number of interacting agents. In so doing, I provide further evidence that the existence of local interactions can change the aggregate behavior of an economic system in fundamental ways, and that the form of that interaction has important implications for its dynamic properties.

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Bibliographic Info

Paper provided by EconWPA in its series Game Theory and Information with number 9809006.

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Length: 36 pages
Date of creation: 30 Sep 1998
Date of revision: 01 Oct 1998
Handle: RePEc:wpa:wuwpga:9809006

Note: Type of Document - pdf; prepared on IBM PC; pages: 36; figures: in separate file (iife_graphs.pdf)
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Web page: http://128.118.178.162

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  1. Brock,W.A. & Durlauf,S.N., 2000. "Discrete choice with social interactions," Working papers 7, Wisconsin Madison - Social Systems.
  2. Keenan, Donald C. & O'Brien, Mike J., 1993. "Competition, collusion, and chaos," Journal of Economic Dynamics and Control, Elsevier, vol. 17(3), pages 327-353, May.
  3. Scott, A. & Acemoglu, D., 1995. "Asymmetric Business Cycles: Theory and Time-series Evidence," Economics Series Working Papers 99173, University of Oxford, Department of Economics.
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  7. Jovanovic, Boyan, 1987. "Micro Shocks and Aggregate Risk," The Quarterly Journal of Economics, MIT Press, vol. 102(2), pages 395-409, May.
  8. Haller, Hans, 1990. "Large random graphs in pseudo-metric spaces," Mathematical Social Sciences, Elsevier, vol. 20(2), pages 147-164, October.
  9. L. Blume, 2010. "The Statistical Mechanics of Strategic Interaction," Levine's Working Paper Archive 488, David K. Levine.
  10. Steven N. Durlauf, 1991. "Multiple Equilibria and Persistence in Aggregate Fluctuations," NBER Working Papers 3629, National Bureau of Economic Research, Inc.
  11. Hans Haller, 1990. "Large Random Graphs in Pseudo-Metric Spaces," Discussion Paper Serie A 301, University of Bonn, Germany.
  12. Randal J. Verbrugge, 1998. "Local Complementarities and Aggregate Fluctuations," Macroeconomics 9809016, EconWPA, revised 30 Sep 1998.
  13. Brock, William A. & Sayers, Chera L., 1988. "Is the business cycle characterized by deterministic chaos?," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 71-90, July.
  14. Kirman, Alan, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, MIT Press, vol. 108(1), pages 137-56, February.
  15. Scheinkman, Jose A, 1990. "Nonlinearities in Economic Dynamics," Economic Journal, Royal Economic Society, vol. 100(400), pages 33-48, Supplemen.
  16. Follmer, Hans, 1974. "Random economies with many interacting agents," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 51-62, March.
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