Pareto-Efficient Multi-Buyer Mechanisms: Characterization, Fairness and Welfare
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917270677094400 |
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| author | Babaioff, Moshe Chen, Sijin Chen, Zhaohua Feng, Yiding |
| author_facet | Babaioff, Moshe Chen, Sijin Chen, Zhaohua Feng, Yiding |
| contents | A truthful mechanism for a Bayesian single-item auction results with some ex-ante revenue for the seller, and some ex-ante total surplus for the buyers. We study the Pareto frontier of the set of seller-buyers ex-ante utilities, generated by all truthful mechanisms when buyers values are sampled independently and identically (i.i.d.). We first provide a complete structural characterization of the Pareto frontier under natural distributional assumptions. For example, when valuations are drawn i.i.d. from a distribution that is both regular and anti-MHR, every Pareto-optimal mechanism is a second-price auction with a reserve no larger than the monopoly reserve.
Building on this, we interpret the problem of picking a mechanism as a two-sided bargaining game, and analyze two canonical Pareto-optimal solutions from cooperative bargaining theory: the Kalai-Smorodinsky (KS) solution, and the Nash solution. We prove that when values are drawn i.i.d. from a distribution that is both regular and anti-MHR, in large markets both solutions yield near-optimal welfare. In contrast, under worst-case MHR distributions, their performance diverges sharply: the KS solution guarantees one-half of the optimal welfare, while the Nash solution might only achieve an arbitrarily small fraction of it. These results highlight the sensitivity of fairness-efficiency tradeoffs to distributional structure, and affirm the KS solution as the more robust notion of fairness for asymmetric two-sided markets. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_11967 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pareto-Efficient Multi-Buyer Mechanisms: Characterization, Fairness and Welfare Babaioff, Moshe Chen, Sijin Chen, Zhaohua Feng, Yiding Computer Science and Game Theory A truthful mechanism for a Bayesian single-item auction results with some ex-ante revenue for the seller, and some ex-ante total surplus for the buyers. We study the Pareto frontier of the set of seller-buyers ex-ante utilities, generated by all truthful mechanisms when buyers values are sampled independently and identically (i.i.d.). We first provide a complete structural characterization of the Pareto frontier under natural distributional assumptions. For example, when valuations are drawn i.i.d. from a distribution that is both regular and anti-MHR, every Pareto-optimal mechanism is a second-price auction with a reserve no larger than the monopoly reserve. Building on this, we interpret the problem of picking a mechanism as a two-sided bargaining game, and analyze two canonical Pareto-optimal solutions from cooperative bargaining theory: the Kalai-Smorodinsky (KS) solution, and the Nash solution. We prove that when values are drawn i.i.d. from a distribution that is both regular and anti-MHR, in large markets both solutions yield near-optimal welfare. In contrast, under worst-case MHR distributions, their performance diverges sharply: the KS solution guarantees one-half of the optimal welfare, while the Nash solution might only achieve an arbitrarily small fraction of it. These results highlight the sensitivity of fairness-efficiency tradeoffs to distributional structure, and affirm the KS solution as the more robust notion of fairness for asymmetric two-sided markets. |
| title | Pareto-Efficient Multi-Buyer Mechanisms: Characterization, Fairness and Welfare |
| topic | Computer Science and Game Theory |
| url | https://arxiv.org/abs/2602.11967 |