{"type":"ScholarlyArticle","title":"Prophet Inequalities for Bayesian Persuasion","authors":[{"name":"Niklas Hahn","slug":"niklas-hahn","given":"Niklas","family":"Hahn","affiliation":"Goethe University Frankfurt , Germany"},{"name":"Martin Hoefer","slug":"martin-hoefer","given":"Martin","family":"Hoefer","affiliation":"Goethe University Frankfurt , Germany"},{"name":"Rann Smorodinsky","slug":"rann-smorodinsky","given":"Rann","family":"Smorodinsky","affiliation":"Technion , Israel"}],"abstract":"We study an information-structure design problem (i.e., a Bayesian persuasion problem) in an online scenario. Inspired by the classic gambler's problem, consider a set of candidates who arrive sequentially and are evaluated by one agent (the sender). This agent learns the value from hiring the candidate to herself as well as the value to another agent, the receiver. The sender provides a signal to the receiver who, in turn, makes an irrevocable decision on whether or not to hire the candidate. A-priori, for each agent the distribution of valuation is independent across candidates but may not be identical. We design good online signaling schemes for the sender. To assess the performance, we compare the expected utility to that of an optimal offline scheme by a prophet sender who knows all candidate realizations in advance. We show an optimal prophet inequality for online Bayesian persuasion, with a 1/2-approximation when the instance satisfies a \"satisfactory-status-quo\" assumption. Without this assumption, there are instances without any finite approximation factor. We extend the results to combinatorial domains and obtain prophet inequalities for matching with multiple hires and multiple receivers.","doi":"10.24963/ijcai.2020/25","url":"https://ijcai.org/proceedings/2020/25","pdf":"https://ijcai.org/proceedings/2020/0025.pdf","markdown":"https://ijcai.org/proceedings/2020/25.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/25","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":25,"pages":{"first":175,"last":181},"keywords":["Agent-based and Multi-agent Systems: Agent Communication","Agent-based and Multi-agent Systems: Algorithmic Game Theory"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/24985/file_24985.m3u8","length_sec":279,"provider":"hls"}],"references":[{"position":1,"raw":"[Alaei, 2014] Saeed Alaei. 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