Discounted network Myerson value and an application in power grid management

The classical Myerson value for network games assigns payoffs to the players in a network based on their productivity in it. This often results in an unequal distribution of the resources generated by the players in the network. However, when link formation is costly but essential for generating resources in the network, one way of keeping the network stable is to incentivize those lesser-paid players with discounts. In this paper, we introduce a new allocation rule called the delta-discounted network Myerson value for network games, inheriting a similar idea from cooperative game theory. This value allows the designer to control the discounting amount by adjusting the discount parameter delta. We provide two characterizations of this value and discuss an application in the power grid management problem that specifies how this value can help sustainably transport green energy.