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 outcome p[subscript c] and the bilateral bargaining outcome p[subscript b] are possible in subgame perfect equilibrium. We consider two variations. First, if there is a cost larger that p[subscript c]-p[subscript b] to the seller of changing partner, p[subscript b] is the unique outcome, otherwise no restriction expires. In the second variation the seller makes an Epsilon-binding preannouncement of whether he will change buyers after disagreement. If Epsilon is small there are equilibrium prices close to p[subscript b]. But for any Epsilon, if the discount factor is close to 1, the unique equilibrium price is p[subscript c].