Rubinstein and Wolinsky (1990) study a market with one seller, two buyers, and voluntary matching. Both the competitive outcomepc and the bilateral bargaining outcomepb are possible in subgame perfect equilibrium. We consider two variations. First, if there is a cost larger thanpc−pc to the seller of changing partner,pc is the unique outcome, otherwise no restriction expires. In the second variation the seller makes anε-binding preannouncement of whether he will change buyer after disagreement. Ifε is small there are equilibrium prices close topc. But for anyε, if the discount factor is close to 1, the unique equilibrium price ispc.
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