[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84395-en":3,"doc-seo-84395-105":30,"detail-sidebar-cat-0-en-105":91},{"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},84395,7971461741311,"Ophelia","https://ap-avatar.wpscdn.com/avatar/74000253aff267980c6?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779345379180704826",8,"Research & Report","Multi-Sender Bayesian Persuasion with Imperfect Information","Multi-sender Bayesian persuasion studies one receiver interacting with several strategic senders under imperfect information. The joint ground state has multiple components, privately observed by different senders, while the receiver holds a common prior over the joint space. Senders simultaneously choose signaling policies, and the receiver acts using a posterior induced by sampled signals. The paper analyzes equilibrium behavior under the receiver’s straightforward policy, characterizes sender best responses, and identifies prior conditions that yield fully informative equilibria. It further shows that receiver commitment to generalized action policies fundamentally changes outcomes, enabling fully informative equilibria for any prior.","arXiv :2607 .08675v 1 [ cs .GT] 9 Jul 2026  \nMulti-Sender Bayesian Persuasion with Imperfect Information  \nAndra Siva Sai Teja ∗ Ganesh Ghalme† Sujit Gujar ‡  \nJuly 10, 2026  \nAbstract  \nWe study a multi-sender Bayesian persuasion problem with one receiver and several strategic senders.  \nThe underlying ground state has multiple components, each privately observed by a different sender, while the receiver holds a common prior over the joint state space. Senders simultaneously choose signaling policies, and the receiver takes an action based on the posterior induced by signals; each sampled independently from sender signalling policies. We analyze the game induced by the receiver’s straightforward policy, which selects a receiver-optimal action at every posterior. In particular, we characterize the senders’ best responses under straightforward policy and identify conditions on the prior which induce fully informative equilibrium; i.e., truthfully reporting the ground truth is an equilibrium strategy for every sender. These conditions capture cases where senders’ incentives are sufficiently aligned for full revelation to arise without additional receiver commitment.  \nThe important contribution of this paper is to analyze games induced by a more general (possibly randomized) class of action policies committed by the receiver before senders choose their signalling strategies. We show that this commitment power fundamentally changes the problem. In particular, we show that for any prior over the joint state space, the receiver can construct action policies that maximize her payoff while ensuring a fully informative equilibrium.  \n1 Introduction  \nBayesian persuasion (BP), introduced by Kamenica and Gentzkow [2011], is a framework characterized by asymmetric information between two parties: a sender and a receiver. In this setting, a more informed sender (he) communicates with the receiver (she) by sending a signal. While the true state of the world is privately observed by the sender, he can strategically reveal this information to the receiver, who takes a payoff-relevant action that affects both parties. The receiver is considered Bayesian rational ; that is, she takes an action based on the posterior beliefs induced by a signal sampled from the signaling policy committed by the sender. We call such action a straightforward policy. An important question is whether the sender can effectively persuade the receiver to take an action that benefits him. That is, it maximizes the sender’s expected payoff under the posterior belief distribution induced by a signaling policy, given the receiver’s straightforward action policy. The classical concavification result of Kamenica and Gentzkow [2011] answers this question positively by fully characterizing the payoffs under induced posterior distributions.  \nIn this paper, we consider multiple senders and one receiver. We refer to this setting as Comp-BP or Competitive Bayesian Persuasion. In Comp-BP, the receiver’s action affects the payoff of all the players.  \n∗ IIT Hyderabad [ai22mtech11001@iith.ac.in](ai22mtech11001@iith.ac.in)  \n†[IIT Hyderabad](IIT Hyderabad ganeshghalme@ai.iith.ac.in)[ ganeshghalme@ai.iith.ac.in](IIT Hyderabad ganeshghalme@ai.iith.ac.in)  \n‡IIIT Hyderabad [sujit.gujar@iiit.ac.in](sujit.gujar@iiit.ac.in)  \nThis leads to a situation in which a given sender’s signaling strategy depends on the signaling strategies of other senders through the posterior induced by the joint signal. The interplay among multiple senders’pursuits makes the problem challenging.  \nThe Comp-BP setting arises in many real-world scenarios involving competition under asymmetric information. One example is two sellers offering similar goods with privately known quality, each strategically signaling to attract a buyer. Another example is job recommendation processes, where advisors endorse their own students for a single position while having limited information about competing candidates. Similar dy","cbCaipgpD4CwK0fZ","https://ap.wps.com/l/cbCaipgpD4CwK0fZ","pdf",498533,4,1,16,"English","en",105,"# Introduction\n## Multi-sender Bayesian persuasion framework\n## Key differences from classical Bayesian persuasion\n## Contributions","[{\"question\":\"What is the core model studied in the paper?\",\"answer\":\"The paper studies a competitive multi-sender Bayesian persuasion game with one receiver and multiple strategic senders, where each sender privately observes a component of the joint ground state and chooses a signaling policy.\"},{\"question\":\"How does the receiver choose an action after receiving signals?\",\"answer\":\"The receiver selects an action based on the posterior belief induced by signals, including analysis of a straightforward policy that chooses a receiver-optimal action at every posterior.\"},{\"question\":\"What effect does the receiver’s commitment power have?\",\"answer\":\"By committing upfront to a (possibly randomized) action policy, the receiver fundamentally changes the problem structure; the paper shows that for any prior over the joint state space, the receiver can construct action policies that maximize her payoff while still enabling a fully informative equilibrium.\"}]",1784195299,40,{"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":86,"head_meta":88,"extra_data":90,"updated_unix":28},"multi-sender-bayesian-persuasion-with-imperfect-information","",{"@graph":36,"@context":85},[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/multi-sender-bayesian-persuasion-with-imperfect-information/84395/",{"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",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is the core model studied in the paper?","Question",{"text":75,"@type":76},"The paper studies a competitive multi-sender Bayesian persuasion game with one receiver and multiple strategic senders, where each sender privately observes a component of the joint ground state and chooses a signaling policy.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the receiver choose an action after receiving signals?",{"text":80,"@type":76},"The receiver selects an action based on the posterior belief induced by signals, including analysis of a straightforward policy that chooses a receiver-optimal action at every posterior.",{"name":82,"@type":73,"acceptedAnswer":83},"What effect does the receiver’s commitment power have?",{"text":84,"@type":76},"By committing upfront to a (possibly randomized) action policy, the receiver fundamentally changes the problem structure; 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