In game theory, a convex game is one in which the incentives for joining a coalition increase as the coalition grows. This paper shows that the core of such a game -- the set of outcomes that cannot be improved on by any coalition of players -- is quite large and has an especially regular structure. Certain other cooperative solution concepts are also shown to be related to the core in simple ways: (1) The value of a convex game is the center of gravity of the extreme points of the core, and (2) the von Neumann-Morgenstern stable set solution of a convex game is unique and coincides with the core. Similar results for the kernel and the bargaining set will be presented in a later paper. Here, it is also shown that convex games are not necessarily the sum of any number of convex measure games.
Shapley, Lloyd S., Cores of Convex Games. Santa Monica, CA: RAND Corporation, 1971. https://www.rand.org/pubs/papers/P4620.html. Also available in print form.
Shapley, Lloyd S., Cores of Convex Games, RAND Corporation, P-4620, 1971. As of November 29, 2023: https://www.rand.org/pubs/papers/P4620.html