In an information graph situation, some agents that are connected by an undirected graph can share with no cost some information or technology that can also be obtained from a source. If an agent is not connected to an informed player, this agent pays a unitary cost to obtain this technology. A coalitional cost game can be defined from this situation, and the core of this game is known to be non- empty. We prove that the core of an information graph game is a von Neumann-Morgenstern stable set if and only if the graph is cycle- complete, or equivalently if the information graph game is concave. When the graph is not cycle-complete, whether there always exists a stable set is an open question. In this regard, we show that if the information graph consists of a ring that contains the source, then a stable set always exists and it is the core of a related information graph situation where one edge has been deleted.

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