84 Implementation of the Nash solution 1. INTRODUCTION The complex title of this article describes precisely its contents and goals, but it hides the enormous importance of the underlying problem of allocating justly the available resources among a population of individual agents. Our problem in its most simple form is the problem of fair division of some divisible object among two persons. Here“fair” is a non-technical term whose formal specification depends on the situation and on potential property rights of the negotiating persons. Accordingly, either distribution or exchange may best describe the activity to be analyzed. Although this fundamental problem of bilateral negotiation is still at the heart of economics and game theory, it has a very long history. This is competently and transparently described by Dos Santos Ferreira(2002) who, referring to Stuart(1982) and Burnet(1900), traces back modern treatments of bilateral exchange and bargaining to Aristotle’s(ca. 335..) Nichomachean Ethics . He argues convincingly that the underlying ideas about proportionality and the arithmetic and geometric means of modern axiomatic bargaining solutions can be traced back to Aristotle’s analysis. Dos Santos Ferreira(2002, p. 568) considers“The Nichomachean Ethics in which Aristotle presents his analysis of bilateral exchange” as“undoubtedly one of the most influential writings in the whole history of economic thought” that“through the commentaries of Albertus Magnus and ... of his pupil Thomas Aquinas ... was one of the main sources of the Scholastic doctrine of just prices.” He then follows this influence via Turgot(1766, 1769), Marx (1867), Menger(1871), and Edgeworth(1881) to the modern treatments, in particular the seminal contributions by Nash(1950, 1953) and Rubinstein (1982) underlying our present analysis. Shubik(1985) mentions the‘horse market model’ of Bo¨hm-Bawerk(1891) which became the forerunner of assignment games, as another 19th century work concerned with bilateral exchange. The contract curve offered by Edgeworth and the price interval of Bo¨hm-Bawerk reflect the problem of indeterminacy inherent in those early approaches that was only solved by Zeuthen(1930) and Hicks(1932). Harsanyi(1956) compared the modelling of bilateral bargaining before and after the appearance of the theory of games(see Bishop, 1963) and found Zeuthen’s approach, which he presented in the language of game theory, supe­rior to that of Hicks and demonstrated that Zeuthen’s solution coincides with the solution provided by Nash(1950, 1953), who defined and axiomatically Journal of Mechanism and Institution Design (), 2016