In this paper, we develop a supply chain network game theory model with product differentiation, possible outsourcing of production and distribution, and quality and price competition. The original firms compete with one another in terms of in-house quality levels and product flows, whereas the contractors, aiming at maximizing their own profits, engage in competition for the outsourced production and distribution in terms of prices that they charge and their quality levels. The solution of the model provides each original firm with its optimal in-house quality level as well as its optimal in-house and outsourced production and shipment quantities that minimize the total cost and the weighted cost of disrepute, associated with lower quality levels and the impact on a firm's reputation. The governing equilibrium conditions of the model are formulated as a variational inequality problem. An algorithm, which provides a discrete-time adjustment process and tracks the evolution of the product flows, quality levels, and prices over time, is proposed and convergence results given. Numerical examples are provided to illustrate how such a supply chain network game theory model can be applied in practice. The model is relevant to products ranging from pharmaceuticals to fast fashion to high technology products.
