Location of Repository

Local Interactions as a Decentralized Mechanism Coordinating Equilibrium Expectations

By Martin Hohnisch

Abstract

In 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.Sunspot Equilibria, Voter model, local interactions, coordination

OAI identifier:

Suggested articles

Preview

Citations

  1. (1973). A model for spatial conflict,
  2. (1994). A Theory of Conformity,
  3. (1954). A Theory of Social Comparison,
  4. (1974). Core and Equilibria of Large Economies,
  5. (2000). Diffusive Clustering in the Two-Dimensional Voter Model,
  6. (1983). Do Sunspots matter ?,
  7. (2002). Equilibrium Selections, in:
  8. (1975). Ergodic Theorems for weakly interacting systems and the voter model,
  9. (1985). Interacting Particle Systems,
  10. (2003). Macroeconomics and General Equilibrium, in:
  11. (1971). On Random Preferences and Equilibrium Analysis,
  12. (2005). Random Economies and the Concept of Statistical Economics,
  13. (1974). Random Economies with Many Interacting Agents,
  14. (2000). Recurrence and Ergodicity for Interacting Particle Systems, Probability Theory and Related Fields
  15. (1999). Stochastic Interacting Systems,
  16. (1956). Studies of Independence and Conformity: A Minority of One Against a Unanimous Majority,
  17. (1989). Sunspots and Incomplete Financial Markets: The Leading Example, in:
  18. (1975). The Theory of Stochastic Processes II,
  19. Three observations on sunspots and asset redundancy, in: Economic Analysis of Markets
  20. (1992). Transformations of the Commodity Space, Behavioral Heterogeneity, and the Aggregation Problem,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.