Bargaining Foundations for the Outside Option Principle

Organised by

• Department of Economics

We study a bargaining game in which a seller can trade with one of two buyers, who have values h and l (h > l). The outside option principle (OOP) predicts that the seller trades with the high-value buyer with probability converging to 1 at a price converging to max(h=2; l) as players become patient. While this prediction is supported by the Markov perfect equilibrium (MPE), a wide range of trading outcomes may emerge in subgame perfect equilibria (SPEs): in the patient limit, the seller can obtain any price in the interval [h=2; h] (and no other); moreover, allocative inefficiency and costly delay are possible. 

We propose equilibrium refinements less restrictive than Markov behaviour that guarantee trading outcomes consistent with OOP. One refinement requires that a buyer’s relative probability of trade does not increase dramatically following a failed negotiation with that buyer. This refinement implies that the seller receives at least the OOP price. Another refinement requires that the seller does not approach a buyer hoping that negotiations fail. SPEs satisfying both refinements conform with OOP (but need not be MPEs). Our benchmark model features strategic matching by the seller. We provide a parallel analysis for the random matching protocol. Under random matching, prices in SPEs may also rise above and fall below l, but cannot get as low as h=2 when the outside option is binding. A refinement particular to this protocol that supports the OOP predictions requires that a random match should not impact the seller’s payoff excessively.

Co-authors: Dilip Abreu