THE DYNAMICS OF MULTILATERAL EXCHANGE

Abstract

The article formulates a dynamic mathematical model where arbitrarily many players produce, consume, exchange, loan, and deposit arbitrarily many goods over time to maximize utility. Consuming goods constitutes a benefit, and producing, exporting, and loaning away goods constitute a cost. Utilities are benefits minus costs, which depend on the exchange ratios and bargaining functions. Three-way exchange occurs when one player acquires, through exchange, one good from another player with the sole purpose of using this good to exchange against the desired good from a third player. Such a triple handshake is not merely a set of double handshakes since the player assigns no interest to the first good in his benefit function. Cognitive and organization costs increase dramatically for higher order exchanges. An exchange theory accounting for media of exchange follows from simple generalization of two-way exchange. The examples of r-way exchange are the triangle trade between Africa, the USA, and England in the 17th and 18th centuries, the hypothetical hypercycle involving RNAs as players and enzymes as goods, and reaction–diffusion processes. The emergence of exchange, and the role of trading agents are discussed. We simulate an example where two-way exchange gives zero production and zero utility, while three-way exchange causes considerable production and positive utility. Maximum utility for each player is reached when exchanges of the same order as the number of players in society are allowed. The article merges micro theory and macro theory within the social, natural, and physical sciences.