Bargaining Order in a Multi-Person Bargaining Game

This paper studies a complete-information bargaining game with one buyer and multiple sellers of di¤erent ?sizes? or bargaining strengths. The bargaining order is determined by the buyer. If the buyer can commit to a bargaining order, there is a unique subgame perfect equilibrium outcome where the buyer bargains in order of increasing size ? from the smallest to the largest. If the buyer cannot commit to a bargaining order and the sellers are su¢ ciently di¤erent, there is also a unique subgame perfect equilibrium outcome again with the order of increasing size.