Outside option values for network games

Various political, economic and social situations of cooperation and bargaining can be modeled by cooperative games. Cooperation potential and the outcome of cooperation are often influenced by the structure of how agents are related to each other, that is, by a network structure. Extending Myerson (1977)'s model of restricted communication, Jackson and Wolinsky (1996) introduced the setting of network games which is more flexible, for example in the distinction between the outcome of communication paths. The contribution of this paper is the analysis of outside-option-sensitive allocation rules in the network game setting. More precisely, we provide definitions and axiomatizations of outside-option-sensitive extensions of the Myerson value and the Position value for network games, the graph-χ-value and the kappa value for network games, respectively. These values have not been analyzed in the network game framework so far and, in contrast to their counterparts by means of restricted communication, we justify the values following the simple aspects used in the original axiomatization of the Shapley value. In addition, we also find such a justification of the Myerson value for network games. In all axiomatizations, we do not require any conditions on the network.