The network equilibrium problem in integers

In the usual approach to network equilibrium models, the flow variables are modeled as continuous. When the problem under study involves discrete decision makers each controlling an indivisible unit of flow, another approach is called for. We treat the problem as an n‐person noncooperative game with pure strategies corresponding to feasible paths through the network. It is shown that pure‐strategy Nash equilibria exist and that any solution to an integer‐variable analogue of the usual network equilibrium model is such a Nash equilibrium. It is also shown that when individuals can control more than a single unit of flow and want to minimize the sum of their costs, pure‐strategy Nash equilibria do not necessarily exist.