Selling an Item Among a Strategic Bidder and a Profiled Agent
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908499713196032 |
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| author | Caragiannis, Ioannis Kalantzis, Georgios |
| author_facet | Caragiannis, Ioannis Kalantzis, Georgios |
| contents | We consider the fundamental scenario where a single item is to be sold to one of two agents. Both agents draw their valuation for the item from the same probability distribution. However, only one of them submits a bid to the mechanism. The other agent is profiled, i.e., the mechanism receives a prediction for her valuation, which can be true or false. Our goal is to design mechanisms for selling the item that make as much revenue as possible in cases of a correct or incorrect prediction. As a benchmark for proving our revenue-approximation guarantees, we use the maximum expected revenue that can be obtained by a strategic and an honest bidder. We study two mechanisms. The first one yields optimal revenue when the prediction is guaranteed to be correct and a constant revenue approximation when the prediction is incorrect, assuming that the agent valuations are drawn from a monotone hazard rate (MHR) distribution. The second mechanism ignores the prediction for the second agent and simulates the revenue-optimal mechanism when no bid information for the bidders is available. We prove, again assuming that valuations are drawn from MHR distributions, that this mechanism achieves a constant revenue approximation guarantee compared to our revenue benchmark. The MHR assumption is necessary; we show that there are non-MHR but regular probability distributions for which no constant approximation of our revenue benchmark is possible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_12313 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Selling an Item Among a Strategic Bidder and a Profiled Agent Caragiannis, Ioannis Kalantzis, Georgios Computer Science and Game Theory We consider the fundamental scenario where a single item is to be sold to one of two agents. Both agents draw their valuation for the item from the same probability distribution. However, only one of them submits a bid to the mechanism. The other agent is profiled, i.e., the mechanism receives a prediction for her valuation, which can be true or false. Our goal is to design mechanisms for selling the item that make as much revenue as possible in cases of a correct or incorrect prediction. As a benchmark for proving our revenue-approximation guarantees, we use the maximum expected revenue that can be obtained by a strategic and an honest bidder. We study two mechanisms. The first one yields optimal revenue when the prediction is guaranteed to be correct and a constant revenue approximation when the prediction is incorrect, assuming that the agent valuations are drawn from a monotone hazard rate (MHR) distribution. The second mechanism ignores the prediction for the second agent and simulates the revenue-optimal mechanism when no bid information for the bidders is available. We prove, again assuming that valuations are drawn from MHR distributions, that this mechanism achieves a constant revenue approximation guarantee compared to our revenue benchmark. The MHR assumption is necessary; we show that there are non-MHR but regular probability distributions for which no constant approximation of our revenue benchmark is possible. |
| title | Selling an Item Among a Strategic Bidder and a Profiled Agent |
| topic | Computer Science and Game Theory |
| url | https://arxiv.org/abs/2502.12313 |