Pure Competition, Coalitional Power, and Fair Division

Abstract

Abstract : Consideration of a new application of the mathematical theory of games to the conceptual foundations of the theory of economic competition. The Memorandum first gives a nontechnical discussion of three different types of solution to mathematical models of the marketplace, namely, the competitive equilibrium, the core, and the value, and relates them to three principles of distribution, namely, pure competition, coalitional power, and fair division. Several models are then analyzed in detail. First, numerical solutions are calculated for a class of symmetric market games, chosen to contrast the value with the other two solutions. Next, as the number of traders is increased, the convergence of all three solutions to a single outcome is proved for a general class of markets with money. Finally, an illustrative market model without money is evaluated explicitly as a function of the size of the market. This represents the first substantial application of a new definition of the value for games without side payments. The formal definitions are summarized in an appendix. (Author)

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