Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Mar, 2024, Volume 92, Issue 2

Bargaining and Exclusion with Multiple Buyers
p. 429-465

Dilip Abreu, Mihai Manea

A seller trades with q out of n buyers who have valuations a1 ≥ a2 ≥ ⋯ ≥ an > 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 maxlq+1[(a1+a2+⋯+al−1)/2+al+1+⋯+aq+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 ai/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.

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Supplemental Material

Supplement to "Bargaining and Exclusion with Multiple Buyers"

Dilip Abreu and Mihai Manea

This supplement contains material not found within the manuscript.