[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86346-en":3,"doc-seo-86346-105":30,"detail-sidebar-cat-0-en-105":83},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},86346,1099513958607,"Jiven","https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399",8,"Research & Report","Leakage-Robust Bayesian Persuasion","Leakage-robust Bayesian persuasion sits between public and private Bayesian persuasion by modeling scenarios where a sender’s privately communicated signals may be leaked to other receivers. The work designs leakage-robust signaling schemes and evaluates robustness costs using two measures. k-worst-case persuasiveness bounds the gap from optimal private persuasion under up to k leaked signals, while expected downstream utility robustness quantifies the degradation after receivers best respond under leakage randomness. It further shows subsampling and masking can transform private schemes with minmax optimal loss.","arXiv :2411 . 16624v2 [ cs .GT] 11 Jul 2026  \nLeakage-Robust Bayesian Persuasion ∗  \nNika Haghtalab† Mingda Qiao‡ Kunhe Yang§  \nAbstract  \nThis paper introduces the concept of leakage-robust Bayesian persuasion. Situated between public Bayesian persuasion [29] (and its multi-receiver variants [16, 42]) and private Bayesian persuasion [2], leakage-robust persuasion considers a setting where one or more signals privately communicated by a sender to the receivers may be leaked. We study the design of leakage-robust Bayesian persuasion schemes and quantify the price of robustness using two formalisms:  \n- The first notion, k-worst-case persuasiveness, requires a signaling scheme to remain persuasive as long as each receiver observes no more than k leaked signals from other receivers. We quantify the Price of Robust Persuasiveness (PoRPk)—i.e., the gap in sender’s utility as compared to the optimal private persuasion scheme—as Θ(min{2k , n}) for supermodular sender utilities and Θ(k) for submodular or XOS sender utilities, where n is the number of receivers. This result also establishes that in some instances, Θ(log k) leakages are sufficient for the utility of the optimal leakage-robust persuasion to degenerate to that of public persuasion.  \n- The second notion, expected downstream utility robustness, relaxes the persuasiveness requirement and instead considers the impact on sender’s utility resulting from receivers best responding to their observations. By quantifying the Price of Robust Downstream Utility (PoRU) as the gap between the sender’s expected utility over the randomness in the leakage pattern as compared to private persuasion, our results show that, over several natural and structured distributions of leakage patterns, PoRU improves PoRP to Θ(k) or even Θ(1), where k is the maximum number of leaked signals observable to each receiver across leakage patterns in the distribution.  \nEn route to these results, we show that subsampling and masking serve as general-purpose algorithmic paradigms for transforming any private persuasion signaling scheme to one that is leakage-robust, with minmax optimal loss in sender’s utility.  \n∗ A preliminary version was accepted at the 26th ACM Conference on Economics and Computation (EC 2025) .†UC Berkeley. Email: [nika@berkeley.edu](nika@berkeley.edu).  \n‡MIT. Email: [mingda.qiao.cs@gmail.com](mingda.qiao.cs@gmail.com. Part)[. Part](mingda.qiao.cs@gmail.com. Part) of this work was done while the author was at UC Berkeley.  \n§UC Berkeley. Email: [kunheyang@berkeley.edu](kunheyang@berkeley.edu).  \n1 Introduction  \nBayesian persuasion, introduced by Kamenica and Gentzkow [29], is a framework for studying the fundamental problem of persuading rational agents by controlling their informational environment. For example, consider a prosecutor who knows more about whether a defendant is guilty and aims to convince a jury to convict. By carefully designing the investigation—deciding whom to subpoena, what questions to ask an expert witness, and which forensic tests to conduct—the prosecutor can influence the jury’s belief in favor of conviction.1 Similarly, in online advertising, a seller with more information about a product’s quality seeks to persuade potential buyers to make a purchase. By designing advertisements that selectively highlight certain aspects of the product, the seller can influence buyers’ purchasing decisions. Bayesian persuasion abstracts these choices by modeling the actions of the prosecutor or seller as the design of signaling schemes, i.e., structured distributions of information or action recommendations conditioned on the true state of the world, that only partially reveal the truth. Bayesian receivers, such as buyers and the jury, then update their beliefs according to the signals generated from these schemes. The design and effectiveness of these signaling schemes has been the main subject of research on Bayesian persuasion.  \nThe effectiveness of Bayesian persuasion ","cbCaifShBX7Qnqok","https://ap.wps.com/l/cbCaifShBX7Qnqok","pdf",674978,4,1,43,"English","en",105,"# Abstract\n# Introduction\n## Public vs. private Bayesian persuasion\n## Signal leakage and robustness threats\n## Paper contributions and robustness notions","[{\"question\":\"What is the purpose of subsampling and masking in the proposed approach?\",\"answer\":\"The paper shows that subsampling and masking are general-purpose algorithmic paradigms to transform any private persuasion signaling scheme into a leakage-robust one, achieving minmax optimal loss in sender utility.\"}]",1784210700,108,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":78,"head_meta":80,"extra_data":82,"updated_unix":28},"leakage-robust-bayesian-persuasion","",{"@graph":36,"@context":77},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":20},"https://docshare.wps.com/document/leakage-robust-bayesian-persuasion/86346/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-27","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71],{"name":72,"@type":73,"acceptedAnswer":74},"What is the purpose of subsampling and masking in the proposed approach?","Question",{"text":75,"@type":76},"The paper shows that subsampling and masking are general-purpose algorithmic paradigms to transform any private persuasion signaling scheme into a leakage-robust one, achieving minmax optimal loss in sender utility.","Answer","https://schema.org",{"og:url":52,"og:type":79,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":81,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":84},[85,89,93,97,102,107,112,115,120,123,127],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":86,"show_sort_weight":87,"slug":88},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":90,"show_sort_weight":91,"slug":92},"Literature",80,"literature",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Exam",70,"exam",{"id":98,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},5,"Comic",60,"comic",{"id":103,"doc_module":4,"doc_module_name":46,"category_name":104,"show_sort_weight":105,"slug":106},6,"Technology",50,"technology",{"id":108,"doc_module":4,"doc_module_name":46,"category_name":109,"show_sort_weight":110,"slug":111},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":113,"slug":114},30,"research-report",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":46,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":98,"slug":130},19,"General","general"]