Manufacturers’ coalition under a price elastic market – a quadratic production game approach

Abstract

The paper addresses a supply network design problem in which a set of enterprises decides to organise itself as a multi-stage supply network by resource sharing and production coordination. A biform game theory formulation of the problem is obtained by combining the cooperative sub-game in the manufacturing network with the strategic sub-game of the Stackelberg type between the retailer and the manufacturers’ network. As a result of the interaction between these two sub-games, a new type of cooperative game, the quadratic production game, is formulated to describe the supply network design problem under anticipated price elastic demands from the market. The key problem of coalitional stability is addressed through the properties of rationality and fairness of the profit sharing agreement. We prove that the game is non-convex in general and thus, the fair solution given by the Shapley value allocation is not always rational. It is proposed to reinforce the coalition stability by selecting a minimal set of partner enterprises achieving the maximal expected profit and applying a profit sharing policy with guaranteed fairness restricted to the member enterprises.