Supply network formation as a biform game

In the context of fixed market prices for the selected set of goods to be manufactured, supply network formation problems have been previously analyzed as cooperative linear production games. In particular, the profit sharing problem among partners of the winning coalition has been solved by a perfectly competitive solution, called the Owen set. Now, if an enterprise network decides to organize itself as a supply chain and imposes the wholesale price of its manufactured goods, then the supply chain design problem under a price elastic random demand from the market can be formulated as a biform game, combining a strategic subgame with a cooperative subgame. The decision variables of the strategic subgame are the wholesale prices and the retail prices of the goods, while the results of the cooperative subgame are the winning coalition and the payoff profile associated with it. The optimal global value function is then computed as the solution of a quadratic programming problem. In this scheme, the enterprise network plays the role of the Stackelberg leader and the retailer the role of the follower. The paper studies this type of biform games. In particular, it shows the existence of a payoff policy that is fair, efficient and individually rational.