Equilibrium in competing Supply-Demand flow problems

In this work, we consider a basic version of the Supply-Demand Flow Problem with a set of clients whose demand has to be satisfied by two sets of production centers, each owned by one agent. The agents want to choose the demand centers optimally according to their own independent objective functions. We formulate the problem of efficiently determining an equilibrium solution. We prove that the solution is Pareto-optimal and equivalent to a Kalai-Smorodinsky solution of a suitably defined bargaining problem. Moreover, the results of a computational study are reported, showing that such an equilibrium provides a good compromise between agents' expectations and a reasonable solution in terms of the total cost experienced by the two agents. The proposed approach fits in many competitive problems arising in the management of distributed supply chains.