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Bargaining Order 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.