On October 14, 2013, Ayse Mutlu Derya will give a talk on "A Characterization of the Myerson Value".
Abstract:
Many problems in game theory are modeled as graphs, where nodes are assumed to represent players and edges (or links) between them are assumed to represent relationships
between the players. One of the main and earliest contributions in network games is due to Myerson (1977), where he adapts the cooperative game theory structures to network structures in which the games are modeled as graphs. Among many others, Myerson’s contribution to allocation rules for networks, named as the Myerson value, is to adapt the Shapley value (1953) which is defined as an allocation rule for cooperative games. Myerson’s characterization is valid for component additive value functions. In this paper, we give a characterization of the Myerson value. Our characterization is valid for all value functions, not just for component additive value functions. We modify our axioms in networks to axioms in cooperative games, and give also a characterization of the Shapley value, which is similar to our characterization of the Myerson value. Two points are worth mentioning. One is that the method we use at our characterization of the Shapley value is pretty similar to Shapley’s original characterization. The other is that similarity of our characterizations of the Myerson value and the Shapley value is not that surprising, yet the similarity contributes how the information changes when one passes from transferable utility games to networks or vice versa.