On the core of linear production games

Abstract

An economic production game is treated, in which players pool resources to produce finished goods which can be sold at a given market price. The production process is linear, so that the characteristic function can be obtained by solving linear programs. Duality theory of linear programming is used to obtain equilibrium price vectors and to prove the non-emptiness of the core. Under replication, it is shown that, in the non-degenerate case, the core converges finitely to the set of competitive equilibria; a counter-example shows that this is not true in the degenerate case (i.e., only convergence in the limit can be guaranteed). © 1975 The Mathematical Programming Society.