Aristotle's analysis of bilateral exchange: an early formal approach to the bargaining problem

Exchange, as analysed by Aristotle in the Nichomachean Ethics, should be viewed as a bilateral relation to be approached not as a market phenomenon but in terms of cooperation between two contractors. This paper accordingly proposes a reconsideration of Aristotle's analysis in the light of modern bargaining theory. This reconsideration reconciles the two principles of distributive and corrective justice as ruling simultaneously exchange relations through the figures of geometric and arithmetic proportions, respectively. It also suggests a new reconstitution of the missing diagram supposedly illustrating Aristotle's analysis, which — contrary to the conventional square endowed with diagonals, used since Albertus Magnus' commentary — fits the function to which such a diagram was probably designed, that of exhibiting Aristotle's solution to the bargaining problem.