Noncooperative General Exchange

by Lloyd S. Shapley

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A game theoretic approach to the problem of monopolistic competition in a general exchange economy, taking account of the effect on prices that individual traders can have through their buy and sell decisions. A noncooperative game in strategic form is defined by designating one good as a "trading money" and letting the players use their initial stock of this good to make bids for the other goods. Prices are determined by dividing the total amount bid for each good by the total supply of that good. A diagrammatic analysis is presented based on the Edgeworth Box, and a number of variants are described that use the same basic bidding process for forming the trading prices. Two theorems are stated (but not proved in this paper) concerning the existence of Nash equilibrium points and their relationship to the competitive equilibrium in markets with many traders. (Presented at the April 1974 Conference on Externalities at Southern Illinois University at Edwardsville; to appear in the Proceedings.)

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