A Theory of Continuum Economies with Independent Shocks and Matchings

Karavaev, Andrei (2008): A Theory of Continuum Economies with Independent Shocks and Matchings.

Abstract

Numerous economic models employ a continuum of negligible agents with a sequence of idiosyncratic shocks and random matchings. Several attempts have been made to build a rigorous mathematical justification for such models, but these attempts have left many questions unanswered. In this paper, we develop a discrete time framework in which the major, desirable properties of idiosyncratic shocks and random matchings hold. The agents live on a probability space, and the probability distribution for each agent is naturally replaced by the population distribution. The novelty of this approach is in the assumption of unknown identity. Each agent believes that initially he was randomly and uniformly placed on the agent space, i.e., the agent's identity (the exact location on the agent space) is unknown to the agent.

• Item Type: MPRA Paper
• Language: English
• Keywords: random matching, idiosyncratic shocks, the Law of Large Numbers, aggregate uncertainty, mixing
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C78 - Bargaining Theory ; Matching Theory; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D83 - Search ; Learning ; Information and Knowledge ; Communication ; Belief ; Unawareness; E - Macroeconomics and Monetary Economics > E0 - General > E00 - General

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