# Bargaining with a Bureaucrat

We consider a bargaining problem where one of the players, the bureaucrat, has the power to dictate any outcome in a given set. The other players, the agents, negotiate with him which outcome to be dictated. In return, the agents transfer some part of their payoffs to the bureaucrat. We state five axioms and characterize the solutions which satisfy these axioms on a class of problems which includes as a subset all submodular bargaining problems. Every solution is characterized by a number α in the unit interval. Each agent in every bargaining problem obtains a weighted average of his individually rational level and his marginal contribution to the set of all players, where the weights are α and 1 - α, respectively. The bureaucrat obtains the remaing surplus. The solution when α = 1/2 is the nucleolus of a naturally related game in characteristic form.