Values of games with probabilistic graphs

In this paper we consider games with probabilistic graphs. The model we dev elop is an extension of the model of games with communication restrictions by Myerson (1977). In the Myerson model each pair of players is joined by a link in the graph if and only if these two players can communicate directl y. The current paper considers a more general setting in which each pair of players has some probability of direct communication. The value is defined and characterized in this context. It is a natural extension of the Myerso n value and it turns out to be the Shapley value of a modified game. (C) 19 99 Elsevier Science B.V. All rights reserved.