Econometrica Vol. 92 No. 2 2024
Bargaining and Exclusion With Multiple Buyers
Abstract
A seller trades with q out of n buyers who have valuations a 1 ≥ a 2 ≥ ⋯ ≥ a n > 0 via sequential bilateral bargaining. When q < n , buyer payoffs vary across equilibria in the patient limit, but seller payoffs do not, and converge to max l ≤ q +1 [( a 1 + a 2 +⋯+ a l −1 )/2+ a l +1 +⋯+ a q +1 ]. If l * is the (generically unique) maximizer of this optimization problem, then each buyer i < l * trades with probability 1 at the fair price a i /2, while buyers i ≥ l * are excluded from trade with positive probability. Bargaining with buyers who face the threat of exclusion is driven by a sequential outside option principle : the seller can sequentially exercise the outside option of trading with the extra marginal buyer q + 1, then with the new extra marginal buyer q , and so on, extracting full surplus from each buyer in this sequence and enhancing the outside option at every stage. A seller who can serve all buyers ( q = n ) may benefit from creating scarcity by committing to exclude some remaining buyers as negotiations proceed. An optimal exclusion commitment , within a general class, excludes a single buyer but maintains flexibility about which buyer is excluded. Results apply symmetrically to a buyer bargaining with multiple sellers.
- DOI
- 10.3982/ecta19675
- Volume
- 92
- Issue
- 2
- Pages
- 429-465
- Language
- en
- Sources
- openalex bibtex:phds-export.bib crossref