Bidding for surplus in network allocation problems

In this paper we study non-cooperative foundations of network allocation rules. We focus on three allocation rules: the Myerson value, the position value and the component-wise egalitarian solution. For any of these three rules we provide a characterization based on component efficiency and some balanced contribution property. Additionally, we present three mechanisms whose equilibrium payoffs are well defined and coincide with the three rules under consideration if the underlying value function is monotonic. Non-monotonic value functions are shown to deal with allocation rules applied to monotonic covers. The mechanisms are inspired by the implementation of the Shapley value by Pérez-Castrillo and Wettstein [Bidding for the surplus: a non-cooperative approach to the Shapley value, J. Econ. Theory 100 (2) (2001) 274–294].