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Bilateral trade is one of the most natural and important forms of economic interaction: A seller has a single, indivisible item for sale, and a buyer is potentially interested. The two parties typically have different, privately known valuations for the item, and ideally, they would like to trade if the buyer values the item more than the seller. The celebrated impossibility result by Myerson and Satterthwaite shows that any mechanism for this setting must violate at least one important desideratum. In this paper, we investigate a richer paradigm of bilateral trade, with many self-interested buyers and sellers on both sides of a single trade who cannot be excluded from the trade. We show that this allows for more positive results. In fact, we establish a dichotomy in the possibility of trading efficiently. If in expectation, the buyers value the item more, we can achieve efficiency in the limit. If this is not the case, then efficiency cannot be achieved in general. En route, we characterize trading mechanisms that encourage truth-telling, which may be of independent interest. We also evaluate our trading mechanisms experimentally, and the experiments align with our theoretical results.
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Bargaining and Exclusion With Multiple Buyers
A seller trades withqout ofnbuyers who have valuationsa1 ≥ a2 ≥ ⋯ ≥ an > 0 via sequential bilateral bargaining. Whenq < n, buyer payoffs vary across equilibria in the patient limit, but seller payoffs do not, and converge to maxl≤q+1[(a1+a2+⋯+al−1)/2+al+1+⋯+aq+1]. Ifl*is the (generically unique) maximizer of this optimization problem, then each buyeri < l*trades with probability 1 at the fair priceai/2, while buyersi ≥ l*are excluded from trade with positive probability. Bargaining with buyers who face the threat of exclusion is driven by asequential outside option principle: the seller can sequentially exercise the outside option of trading with the extra marginal buyerq + 1, then with the new extra marginal buyerq, 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. Anoptimal 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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- PAR ID:
- 10523456
- Publisher / Repository:
- Econometrica
- Date Published:
- Journal Name:
- Econometrica
- Volume:
- 92
- Issue:
- 2
- ISSN:
- 0012-9682
- Page Range / eLocation ID:
- 429 to 465
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3982/ECTA19675
