Sequential Bargaining with Public Intervention: The Optimal Subsidy Path

Abstract

Models of sequential bargaining under asymmetric information often exhibit equilibria which are characterised by the fact that agreement is reached only with a delay and that the final (period) solution is ex ante inefficient. The latter means that agreement is not reached though it is efficient (aggregate pay off exceeds aggregate costs). In this paper we analyse how intervention by a third agent in a sequential bargaining process, modelled as a durable goods monopoly, affects the (high path) equilibrium outcome. The effects of intervention crucially depend on how intervention is formulated. When the intervening agent and the seller decides the price and the subsidy (the intervening agent’s contribution) is decided in a Stackelberg game with the intervening agent as the leader the negotiations are always speeded up and equilibrium inefficiency reduced. When the seller acts as a Stackelberg leader the negotiations are only conditionally speeded up and the equilibrium inefficiency only conditionally reduced. For the same values on the reservation prices and discount factor intervention is more likely to take place when the seller acts as a Stackelberg leader. Also, both the seller’s price and the subsidy are higher when the seller acts as a Stackelberg leader compared to if the intervening agent acts as a Stackelberg leader.