The Shapley value for the network game with pairwise interactions

Abstract

Network games -is new and important part of modern game theory. Networks illustrate the interaction of both individual players and groups. Pairwise interaction is characterized by the ability of players to interact one by one with neighbors in a network. In the paper the analytic expression for the characteristic function is derived. And for special classes of network games the Shapley value is computed.

Cooperative Solutions in Multi-Star Network Games

“…In (Petrosyan and Bulgakova, 2015) and (Bulgakova, 2019), the star model is proposed, and the Shapley value formula is given to study its distribution of income. (Petrosyan and Bulgakova, 2020) is dedicated to the study of multi-stage games with pairwise interactions under the consideration of complete graphs, constructing characteristic functions, and calculating Shapley values.…”