Coincidence of Myerson allocation rule with Shapley value

Abstract

This thesis studies the coincidence of the Myerson allocation rule in the context of networks with the Shapley value in the context of transferable utility games. We start with a value function defined on networks and derive a transferable utility game from that. We show that without any restrictions on the value function, Myerson allocation rule may not lead to the same payoff vector as the Shapley value of the derived TU game for any network. Under the assumption of monotonicity of the value function, we show the existence of such coincidence and examine the relation of the set of networks satisfying this coincidence to the set of pairwise stable and strongly stable networks. Next, we propose a new stability notion and examine the coincidence of the two vectors under this stability notion. Finally an alternative allocation rule is introduced whose payoff vector coincide with the Shapley value of the derived transferable utility game on the set of efficient networks which coincides with the set of strongly stable networks under this allocation rule.