Bargaining order and delays in multilateral bargaining with asymmetric sellers

In a multilateral bargaining problem with one buyer and two heterogeneous sellers owning perfectly complementary units, we find that there exists an equilibrium which leads to inefficient delays when the buyer negotiates with the higher-valuation seller first and where players are extremely impatient. We also find that the buyer prefers to negotiate with the lower-valuation seller first, except in an equilibrium where both the buyer and the lower-valuation seller choose to play strategies that lead negotiations between them to hold out.