On the core of semi-infinite transportation games with divisible goods

The core of games arising from semi-infinite transportation situations with infinitely divisible goods is studied. In these situations one aims at maximizing the profit from transporting a good from a finite number of suppliers to an infinite number of demanders. This good is infinitely divisible. It is shown that the underlying primal and dual infinite programs have no duality gap. Further, there always exist so-called ϵ-core elements in the corresponding cooperative game. Conditions are provided under which the core of the corresponding games is nonempty.