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

On seeking efficient Pareto optimal points in multi-player minimum cost flow problems with application to transportation systems