APPLICATIONS OF GAME THEORY TO ECONOMIC EQUILIBRIUM

Guillermo Owen
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Guillermo Owen: Department of Mathematics, Naval Postgraduate School, Monterey, California, USA 93943, USA

International Game Theory Review (IGTR), 1999, vol. 01, issue 01, 1-8

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.

JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1142/S0219198999000025

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