Finding stable flows in multi-agent networks under an equal-sharing policy

A Multi-Agent network flow problem is addressed in this paper where a set of transportation-agents can control the capacities of a set of routes. Each agent incurs a cost proportional to the chosen capacity. A third-party agent, a customer, is interesting in maximizing the product flow transshipped from a source to a sink node through the network. He offers a reward proportional to the flow value, which is shared equally among the transportation-agents. We address the problem of finding a stable strategy (i.e., a Nash Equilibrium) that maximizes the network flow. In this paper, we present a Mixed Integer Linear Program (MILP) to model and solve this problem.