Balanced games arising from infinite linear models

Kalai and Zemel introduced a class of flow-games showing that these games have a non-empty core and that a minimum cut corresponds to a core allocation. We consider flow-games with a finite number of players on a network with infinitely many arcs: assuming that the total sum of the capacities is finite, we show the existence of a maximum flow and we prove that this flow can be obtained as limit of approximating flows on finite subnetworks. Similar results on the existence of core allocations and core elements are given also for minimum spanning network models (see Granot and Huberman) and semi-infinite linear production models (following the approach of Owen).