Cooperative network flow problem with pricing decisions and allocation of benefits: A game theory approach

Several real problems in telecommunication, transportation, and distribution industries can be analyzed by network flow models. In revenue management, pricing plays a primary role which increases the profit generated from a limited supply of assets. Pricing decision directly affects the amount of service or product demand. Hence, in traditional maximum flow problem, we assume that the demand of sink nodes depends on price of services or products of that nodes. We first develop a mathematical programming model for decision making of pricing by multiple owners in the maximum flow problem. Afterwards, coalitions between owners will be analyzed via different methods of cooperative game theory. A numerical example is given in order to show how these methods suggest appropriate assignments of extra revenue obtained from the cooperation among the owners.