Bargaining Foundations for the Outside Option Principle

• 成果类型: Article; Early Access
• 署名作者: Abreu, Dilip; Manea, Mihai
• 署名单位: New York University; State University of New York (SUNY) System; Stony Brook University
• 刊物名称: REVIEW OF ECONOMIC STUDIES
• ISSN/ISSBN: 0034-6527
• DOI: 10.1093/restud/rdaf053
• 发表日期: 2025
• 关键词: perfect equilibrium; complexity; MARKETS

摘要

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, as players become patient, the seller trades with the high-value buyer with probability converging to 1 at a price converging to max(h/2,l). 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 behavior that guarantee trading outcomes consistent with the OOP. One refinement requires that a buyer's relative probability of trade does not increase dramatically following a failed negotiation with that buyer. Another refinement posits that the seller does not approach a buyer hoping that negotiations fail. SPEs satisfying both refinements conform with the 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 have a narrower range. A refinement particular to this protocol that restores the OOP requires that a random mismatch should not impact the seller excessively.