20 - Paths leading to the Nash set
Published online by Cambridge University Press: 13 October 2009
Summary
Abstract
A dynamic system is constructed to model a possible negotiation process for players facing a (not necessarily convex) pure bargaining game. The critical points of this system are the points where the “Nash product” is stationary. All accumulation points of the solutions of this system are critical points. It turns out that the asymptotically stable critical points of the system are precisely the isolated critical points where the Nash product has a local maximum.
Introduction
J. F. Nash (1950) introduced his famous solution for the class of two-person pure bargaining convex games. His solution was defined by a system of axioms that were meant to reflect intuitive considerations and judgments. The axioms produced a unique one-point solution that turned out to be that point at which the “Nash product” is maximized. Harsanyi (1959) extended Nash's ideas and obtained a similar solution for the class of n-person pure bargaining convex games. (See also Harsanyi 1977, chap. 10.)
Harsanyi (1956) also suggested a procedure, based on the Zeuthen principle, that modeled a possible bargaining process that leads the players to the Nash—Harsanyi point. (See also Harsanyi 1977, chap. 8.)
Recently, in an elegant paper, T. Lensberg (1981) (see also Lensberg 1985) demonstrated that the Nash—Harsanyi point could be characterized by another system of axioms.
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- Information
- The Shapley ValueEssays in Honor of Lloyd S. Shapley, pp. 321 - 330Publisher: Cambridge University PressPrint publication year: 1988
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