# 12-050/1 (2012-05-07)

Author(s)
Rene van den Brink, VU University Amsterdam; Gerard van der Laan, VU University Amsterdam; Nigel Moes, VU University Amsterdam
Keywords:
implementation, cycle-free graph game, tree game, hierarchical outcome, average tree solution, weighted hierarchical outcome
JEL codes:
C71, C72

This discussion paper led to a publication in the 'Journal of Economic Theory', 2014, 148, 2737-2748.

In this note we provide a strategic implementation of the average tree solution for zero-monotonic cycle-free graph games. That is, we propose a non-cooperative mechanism of which the unique subgame perfect equilibrium payoffs correspond to the average hierarchical outcome of the game. This mechanism takes into account that a player is only able to communicate with other players (i.e., to make proposals about a division of the surplus of cooperation) when they are connected in the graph.