Bargaining orders in a multi-person bargaining game

This paper studies a complete-information bargaining game with one buyer and multiple sellers of different “sizes” or bargaining strengths. The bargaining order is determined endogenously. With a finite horizon, there is a unique subgame perfect equilibrium outcome, in which the buyer purchases in order of increasing size-from the smallest to the largest. With an infinite horizon, if the sellers have sufficiently different sizes, there is a unique equilibrium outcome, which has the same bargaining order. If the sellers have similar sizes with an infinite horizon, there may be multiple equilibrium outcomes with different bargaining orders.