Local Interactions as a Decentralized Mechanism Coordinating Equilibrium Expectations
AbstractIn the context of standard two-period pure-exchange economies with sequential trade, this paper proposes a decentralized coordination mechanism for equilibriumexpectations, facilitated by local interactions between agents. Interactions are modelled stochastically by specifying a family of individual Markov processes on a two-dimensional integer lattice Z2 in continuous time. These processes are interdependent, in that the transition rate of each agent’s expectation also depends on expectations of neighboring agents. The particular specification of transition rates chosen in the present paper is known as the (two-dimensional) Voter Model. The composite process has two extremal invariant measures and a continuum of non-extremal invariant measures. The economic content of the stochastic expectations process is twofold. First, the convergence of the expectations process itself constitutes a “sunspot-device”. While convergence to either one of the extremal invariant measures corresponds to a sunspot-free coordination state, convergence to a convex mixture of invariant measures engenders a sunspot equilibrium. Thus, nonergodicity of the expectations process is related to the occurrence of sunspot equilibria. Second, it explains how coordination of expectations is actually achieved through direct interactions between agents. Any particular coordination state (defined as a limiting measure of the process) can be traced back to a set of initial configurations or more general initial distributions of expectations.
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Bibliographic InfoPaper provided by University of Bonn, Germany in its series Bonn Econ Discussion Papers with number bgse30_2005.
Date of creation: Oct 2005
Date of revision:
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Sunspot Equilibria; Voter model; local interactions; coordination;
Find related papers by JEL classification:
- D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
- D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
- D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
- D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
- D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-12-14 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Cass, David & Shell, Karl, 1983. "Do Sunspots Matter?," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 193-227, April.
- Follmer, Hans, 1974. "Random economies with many interacting agents," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 51-62, March.
- Beth Allen & Jayasri Dutta & Haraklis M. Polemarchakis, 1994. "Equilibrium selections," Discussion Paper / Institute for Empirical Macroeconomics 90, Federal Reserve Bank of Minneapolis.
- Hildenbrand, Werner, 1971. "Random preferences and equilibrium analysis," Journal of Economic Theory, Elsevier, vol. 3(4), pages 414-429, December.
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