Bivariate Negotiations as a Problem of Stochastic Terminal Control

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Abstract
A mathematical model is developed for two players negotiating on two negotiation (operational goal) dimensions. Bivanate utilities are not assumed. Rather at any stage the payoff is expressed as a payoff probability distribution stating the probability of a player obtaining various amounts of each of the two variables. The preferred (optimum) payoff distribution is not fixed but changes in the course of negotiations. The model treats concession making as a problem of stochastic terminal control which can be formulated and solved by dynamic programming to yield normative recommendations as to concession making (control). The model is illustrated by numerical example. The present research generalizes work by Rao and Shakun (Rao, A. G., M. F. Shaxun. 1974. A normative model for negotiations. Management Sci. 20 (10, June).) on a single negotiation variable. It models mathematically in the two-player, two-dimensional case negotiation aspects of a general approach to conflict resolution and design of purposeful systems discussed by Shakun (Shakun, M. F. 1981. Formalizing conflict resolution in policy making. Internal. J. Gen. Systems 7 (3); Shakun, M. F. 1981. Policy making and meaning as design of purposeful systems. Internal J. Gen. Systems 7 (4).).

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