A strategic implementation of the sequential equal surplus division rule for digraph cooperative games

We provide a strategic implementation of the sequential equal surplus division rule (B,al et al. in Theory Decis 79:251-283, 2015). Precisely, we design a non-cooperative mechanism of which the unique subgame perfect equilibrium payoffs correspond to the sequential equal surplus division outcome of a superadditive rooted tree TU-game. This mechanism borrowed from the bidding mechanism designed by P,rez-Castrillo and Wettstein (J Econ Theory 100:274-294, 2001), but takes into account the direction of the edges connecting any two players in the rooted tree, which reflects some dominance relation between them. Our proofs rely on interesting properties that we provide for a general class of bidding mechanisms.