  In this paper, we propose a multi-player extension of the minimum cost flow
problem inspired by a transportation problem that arises in modern
transportation industry. We associate one player with each arc of a directed
network, each trying to minimize its cost function subject to the network flow
constraints. In our model, the cost function can be any general nonlinear
function, and the flow through each arc is an integer. We present algorithms to
compute efficient Pareto optimal point(s), where the maximum possible number of
players (but not all) minimize their cost functions simultaneously. The
computed Pareto optimal points are Nash equilibriums if the problem is
transformed into a finite static game in normal form.
