Bargaining in networks and the Myerson value

We focus on a multiperson bargaining situation where the negotiation possibilities for the players are represented by a graph, that is, two players can negotiate directly with each other if and only if they are linked directly in the graph. The value of cooperation among players is given by a TU game. For the case where the graph is a tree and the TU game is strictly convex we present a noncooperative bargaining procedure, consisting of a sequence of bilateral negotiations, for which the unique subgame perfect equilibrium outcome coincides with the Myerson value of the induced graph-restricted game. In each bilateral negotiation, the corresponding pair of players bargains about the difference in payoffs to be received at the end. At the beginning of such negotiation there is a bidding stage in which both players announce prices. The player with the highest price becomes the proposer and makes a take-it-or-leave-it offer in terms of difference in payoffs to the other player. If the proposal is rejected, the proposer pays his announced price to the other player, after which this particular link is eliminated from the graph and the mechanism starts all over again for the remaining graph