On market prices in linear production games

Consider a game in which resources may be combined to produce products of known values. For linear production processes, the game may be characterized by a family of linear programs. It is shown that appropriately defined market prices for the resources coincide with the set of optimal dual solutions to one of these linear programs. This result generalizes and unifies the known cases in game theory, in which the core of a game coincides with the set of dual optimal solutions to a corresponding master linear programming problem.Based on working papers by Engelbrecht-Wiggans (1982) and Granot (1983). The work was motivated by an application, reported in Engelbrecht-Wiggans (1983), supported by the US EPA.Research was partially supported by the Natural Science and Engineering Research Council of Canada Grant A4181.