Decentralized trade with bargaining and voluntary matching

Rubinstein and Wolinsky (1990) study a market with one seller, two buyers, and voluntary matching. Both the competitive outcomep_c and the bilateral bargaining outcomep_b are possible in subgame perfect equilibrium. We consider two variations. First, if there is a cost larger thanp_c−p_c to the seller of changing partner,p_c 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 top_c. But for anyε, if the discount factor is close to 1, the unique equilibrium price isp_c.