Incomplete Information Bargaining with Outside Opportunities
We consider two kinds of "outside opportunity" that a seller of an indivisible good might have: selling to a different buyer and consuming the good herself. In both models the seller is uncertain about the buyer's valuation, and becomes more pessimistic over time. When the seller becomes sufficiently pessimistic, she prefers the outside opportunity, so she will not bargain indefinitely with the current buyer. Despite the resulting finite-horizon nature of negotiations, the link between the buyer's willingness to accept an offer and the seller's eagerness to go "outside" generates multiple equilibria.
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