Approximately Optimal Mechanism Design for Competing Sellers
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912394629873664 |
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| author | Lucier, Brendan Saxena, Raghuvansh R. |
| author_facet | Lucier, Brendan Saxena, Raghuvansh R. |
| contents | Two sellers compete to sell identical products to a single buyer. Each seller chooses an arbitrary mechanism, possibly involving lotteries, to sell their product. The utility-maximizing buyer can choose to participate in one or both mechanisms, resolving them in either order. Given a common prior over buyer values, how should the sellers design their mechanisms to maximize their respective revenues?
We first consider a Stackelberg setting where one seller (Alice) commits to her mechanism and the other seller (Bob) best-responds. We show how to construct a simple and approximately-optimal single-lottery mechanism for Alice that guarantees her a quarter of the optimal monopolist's revenue, for any regular distribution. Along the way we prove a structural result: for any single-lottery mechanism of Alice, there will always be a best response mechanism for Bob consisting of a single take-it-or-leave-it price. We also show that no mechanism (single-lottery or otherwise) can guarantee Alice more than a 1/e fraction of the monopolist revenue. Finally, we show that our approximation result does not extend to Nash equilibrium: there exist instances in which a monopolist could extract full surplus, but neither competing seller obtains positive revenue at any equilibrium choice of mechanisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19453 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximately Optimal Mechanism Design for Competing Sellers Lucier, Brendan Saxena, Raghuvansh R. Computer Science and Game Theory Two sellers compete to sell identical products to a single buyer. Each seller chooses an arbitrary mechanism, possibly involving lotteries, to sell their product. The utility-maximizing buyer can choose to participate in one or both mechanisms, resolving them in either order. Given a common prior over buyer values, how should the sellers design their mechanisms to maximize their respective revenues? We first consider a Stackelberg setting where one seller (Alice) commits to her mechanism and the other seller (Bob) best-responds. We show how to construct a simple and approximately-optimal single-lottery mechanism for Alice that guarantees her a quarter of the optimal monopolist's revenue, for any regular distribution. Along the way we prove a structural result: for any single-lottery mechanism of Alice, there will always be a best response mechanism for Bob consisting of a single take-it-or-leave-it price. We also show that no mechanism (single-lottery or otherwise) can guarantee Alice more than a 1/e fraction of the monopolist revenue. Finally, we show that our approximation result does not extend to Nash equilibrium: there exist instances in which a monopolist could extract full surplus, but neither competing seller obtains positive revenue at any equilibrium choice of mechanisms. |
| title | Approximately Optimal Mechanism Design for Competing Sellers |
| topic | Computer Science and Game Theory |
| url | https://arxiv.org/abs/2505.19453 |