Monge extensions of cooperation and communication structures

Abstract

Cooperation structures without any {\it a priori} assumptions on the combinatorial structure of feasible coalitions are studied and a general theory for mar\-ginal values, cores and convexity is established. The theory is based on the notion of a Monge extension of a general characteristic function, which is equivalent to the Lovász extension in the special situation of a classical cooperative game. It is shown that convexity of a cooperation structure is tantamount to the equality of the associated core and Weber set. Extending Myerson's graph model for game theoretic communication, general communication structures are introduced and it is shown that a notion of supermodularity exists for this class that characterizes convexity and properly extends Shapley's convexity model for classical cooperative games.