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Applications Of Game Theory To Economic Equilibrium

Author

Listed:
  • GUILLERMO OWEN

    (Department of Mathematics, Naval Postgraduate School, Monterey, California, USA 93943, USA)

Abstract

One of the original expectations for the theory of cooperative games was that it would give us results valid for thin markets (where the number of traders is too small for an equilibrium to be reached). Over a period of years, however, it has been shown that, for market games, both the core and the Shapley values converge, in some sense, to the competitive equilibrium. Thus, the feeling arises that for large market games, the game-theoretic concepts yield nothing other than the equilibrium. In this article, we study the question of convergence of the Shapley value to the equilibrium and show that in some cases the convergence can be extremely slow. A very simple example (the "shoe" game) suggests that replacing the value by the equilibrium is in some sense akin to replacing a random variable by its mean.

Suggested Citation

  • Guillermo Owen, 1999. "Applications Of Game Theory To Economic Equilibrium," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 1-8.
  • Handle: RePEc:wsi:igtrxx:v:01:y:1999:i:01:n:s0219198999000025
    DOI: 10.1142/S0219198999000025
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    More about this item

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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