The sigma-core of a cooperative game (Q1174576)

The \(\sigma\)-core of a cooperative game with side-payments is the set of \(\sigma\)-additive elements of the game core. A simple proof of Schmeidler's theorem on the \(\sigma\)-core and core equality conditions are given for exact games. For general monotone games stronger conditions are proved through the conditions of \(\sigma\)-continuity of conjugate game functions. The conditions imply that the function forms a capacity in the sense of Choquet. The results known for capacities are translated into a general \(\sigma\)-core theorem, which in particular gives a necessary and sufficient condition for the non-emptiness of the \(\sigma\)- core.