Stable cores in information graph games

Abstract

In an information graph situation, a finite set of agents and a source are the set of nodes of an undirected graph with the property that two adjacent nodes can share information at no cost. The source has some information (or technology), and agents in the same component as the source can reach this information for free. In other components, some agent must pay a unitary cost to obtain the information. We prove that the core of the derived information graph game is a von Neumann-Morgenstern stable set if and only if the information graph is cycle-complete, or equivalently if the game is concave. Otherwise, whether there always exists a stable set is an open question. If the information graph consists of a ring that contains the source, a stable set always exists and it is the core of a related situation where one edge has been deleted.