Senders

senders

Popular mailbox providers, Google and Yahoo, pioneering the safe email movement, recently put forth new email authentication mandates for email senders. The latest requirements are not only aimed at providing their users with a spam-free inbox but also significantly reducing the risks of direct domain spoofing and email phishing attacks. Email-based cyberattacks have been relentlessly plaguing inboxes, despite various controls enforced by mailbox providers due to the ever-evolving and sophisticated nature of the attacks. Cybercriminals are often successful at bypassing spam filters and creeping their way into the user’s inbox, often impersonating legitimate organizations and individuals. This not only poses an imminent threat to the recipient of these malicious emails but also causes serious damage to the reputation and credibility of the impersonated company. Your Checklist for the New Google and Yahoo Email Sender Requirements Starting early next year (2024), bulk message senders would be expected to adhere to the following requirements: Gmail and Yahoo Email Senders Need to Authenticate Their Emails Message senders often send emails that are not authenticated making it very easy for attackers to impersonate their brand or alter their messages in transit. The renowned mailbox providers recognize that validating email sources is a crucial aspect of email security that will restrict unauthorized messages from reaching their users, and subsequently scamming them. Google and Yahoo have announced the need for bulk senders to authenticate messages using standard email authentication protocols like SPF, DKIM, and . DMARC These industry-acclaimed best practices go a long way in distinguishing between genuine messages and fake ones by verifying the message’s source and content. Businesses are often impersonated in phishing campaigns, wherein their legitimate domain name is forged to send emails on their behalf. These attackers use social engineering to launch highly targeted attacks that have a high success rate. Email authentication, along with other security measures have been proven to be effective strategies in reducing and mitigating a wide range of email-based threats. Emails Should be Easy to Unsubscribe In their latest requirements, Google and Yahoo have stressed the importance of making emails easy to unsubscribe, preferably with a one-click unsubscribe option for recipients. This ensures their users only read emails that they are interested in and filters out those that may be considered spam or unnecessary. While email senders are free to send bulk messages for commercial purposes, an unsubscribe button gives recipients the ability to choose which emails they want to keep receiving and which they don’t. The primary purpose of this stance is to ensure an optimal emailing experience for Gmail and Yahoo users, encouraging them to keep their inboxes spam-free and decluttered. A clean and organized inbox with emails that add value to the users, promotes an active commitment toward customer satisfaction. Emails Should Be Interesting to Receivers Finally, with regard to the last requirement, senders should consider their recipient’s interests while curating the emails they want to send. A two-way approach towards spam reduction wherein on one hand, the recipient is able to easily unsubscribe from your emails, while you curate emails that may actually be of value to your readers - together work in unison to provide an enhanced communication experience that is also effective and beneficial to both parties. The Need for Email Authentication Enforcement: Why Now? Spam is an inbox villain that everyone wants to get rid of. While spam may cause some discomfort and inconvenience, phishing emails are not so merciful. These malicious emails often creep into mailboxes in the garb of a genuine company and spread malware, ransomware or initiate wire transfers. They inflict financial harm upon the victims, while also causing reputational damage to organizations without their knowledge. This is why email authentication is truly the need of the hour with major email service providers extending their support and encouraging adoption with immediate effect. Email Authentication is also taking precedence in other sectors, as the PCI Security Standards Council recently announced DMARC as a mandate for version 4 compliance. To comply, organizations must implement a of at least p=quarantine/reject. DMARC policy While it is a future-dated requirement, organizations are expected to adhere to these latest requirements by March 2025. Get Ready for the Upcoming Google & Yahoo Email Policy Changes - Summary of Requirements To summarize Google and Yahoo’s upcoming email sender requirements, here is a quick checklist that you can refer to: Authenticate your emails against SPF, DKIM, and DMARC Add one-click unsubscription to your emails Send emails that interest your recipients When Does Enforcement Begin? As mentioned by Google and Yahoo, enforcement is projected to begin in February 2024. The Google and Yahoo email policy changes will apply to bulk message senders sending messages to Gmail and/or Yahoo users. You will qualify to fall under the “bulk message sender” category if you send out more than 5000 emails per day. This is a common practice for organizations that frequently send out sales or marketing emails, and the new requirements are aimed at restricting these organizations from spamming the inboxes of recipients with unwanted messages while also protecting them from phishing attacks. Configuring DMARC to Meet Google & Yahoo’s Compliance Mandates From the top level, configuring DMARC and email authentication for your emails may seem like a cakewalk as it simply requires you to publish a DNS TXT record. However, that is just the tip of the iceberg. Technical protocols such as these require granular knowledge of technologies and are easy to get wrong - leading to configuration, syntactical, or other errors. This is why leading organizations fall back on PowerDMARC’s and email authentication services, for an effortless and hassle-free experience. hosted DMARC PowerDMARC Helps You: Meet faster, with automated record generation and setup Google and Yahoo’s email security requirements Monitor and optimize your configurations on a centralized dashboard. Make a smooth transition from DMARC monitoring to enforcement and protect your emails and domain name against spoofing attacks - without compromising on deliverability. Examine detailed insights on your email’s behavior and domain activity with the help of simplified reports, to troubleshoot errors. Mitigate SPF errors 10x more effectively with . SPF Macros Get round-the-clock dedicated assistance from an experienced domain and email security expert. PowerDMARC has helped thousands of customers meet compliance requirements for Google and Yahoo. Complete your checklist before 2024 - sign up for our today! DMARC analyzer

Google & Yahoo Email Senders Must Authenticate Emails by Feb 2024

Google এবং Yahoo ইমেল প্রেরকদের অবশ্যই 2024 সালের ফেব্রুয়ারির মধ্যে ইমেল প্রমাণীকরণ করতে হবে

E-Mail-Absender von Google und Yahoo müssen ihre E-Mails bis Februar 2024 authentifizieren

Los remitentes de correo electrónico de Google y Yahoo deben autenticar los correos electrónicos antes de febrero de 2024

Les expéditeurs d'e-mails Google et Yahoo doivent authentifier leurs e-mails d'ici février 2024

Google और Yahoo ईमेल भेजने वालों को फरवरी 2024 तक ईमेल प्रमाणित करना होगा

Google と Yahoo のメール送信者は 2024 年 2 月までにメールを認証する必要がある

Google 및 Yahoo 이메일 발신자는 2024년 2월까지 이메일을 인증해야 합니다.

Remetentes de e-mail do Google e Yahoo devem autenticar e-mails até fevereiro de 2024

Отправители электронной почты Google и Yahoo должны проверять электронную почту к февралю 2024 г.

Google ve Yahoo E-posta Gönderenlerin Şubat 2024'e Kadar E-postaların Kimlik Doğrulamasını Gerçekleştirmesi Gerekiyor

Người gửi email Google & Yahoo phải xác thực email trước tháng 2 năm 2024

Google 和 Yahoo 电子邮件发件人必须在 2024 年 2 月之前对电子邮件进行身份验证

Cypherpunks Write Code: Len Sassaman & Remailers

সাইফারপাঙ্কস কোড লিখুন: লেন সাসামান এবং রিমেলার

Los cypherpunks escriben código: Len Sassaman y los remailers

Cypherpunks Kirjoita koodi: Len Sassaman & Remailers

Cypherpunks כותבים קוד: Len Sassaman & Remailers

サイファーパンクがコードを書く: レン・サッサマンとリメイラー

Cypherpunks Kokoma Code: Len Sassaman & Ba remailers

Cypherpunks Rašyti kodą: Len Sassaman & Remailers

Cypherpunks د لیکلو کوډ: لین ساسامان او ریمیلرز

Cypherpunks escrevem código: Len Sassaman e Remailers

Шифропанки пишут код: Лен Сассаман и ремейлеры

Cypherpunks Write Code: Len Sassaman සහ Remailers

ሳይፈርፓንክስ ኮድ ጽሓፍ: ሌን ሳሳማን & ሪሜይለርስ

Authors:
(1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu);
(2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu);
(3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 4.3 Multi-phase model and classical Bayesian persuasion Note that the pruned tree will potentially be unbalanced. Lemma 7. Given an N-phase trial M with binary-outcome experiments, if there exists a pruned N-phase trial model P run(M) such that the following two conditions hold, then the sender’s expected utility is given by an equivalent single-phase Bayesian persuasion model. For every non-trivial determined experiment, its sibling is either a trivial or a sender-designed experiment.


There exists a least one sender-designed experiment in each (from root to leaf) experiment sequence of P run(M). References Au, P.H.: Dynamic information disclosure. The RAND Journal of Economics 46(4), 791–823 (2015)


Basu, D.: Statistical information and likelihood [with discussion]. Sankhy¯a: The Indian Journal of Statistics, Series A pp. 1–71 (1975)


Bergemann, D., Morris, S.: Information design: A unified perspective. Journal of Economic Literature 57(1), 44–95 (2019)


Bizzotto, J., R¨udiger, J., Vigier, A.: Dynamic persuasion with outside information. American Economic Journal: Microeconomics 13(1), 179–94 (2021)


Bizzotto, J., Vigier, A.: Can a better informed listener be easier to persuade? Economic Theory 72(3), 705–721 (2021)


Blackwell, D.: Equivalent comparisons of experiments. The annals of mathematical statistics pp. 265–272 (1953)


Dughmi, S., Kempe, D., Qiang, R.: Persuasion with limited communication. In: Proceedings of the 2016 ACM Conference on Economics and Computation. pp. 663–680 (2016)


Dughmi, S., Xu, H.: Algorithmic Bayesian persuasion. SIAM Journal on Computing 50(3), 68–97 (2019)


Ely, J.C.: Beeps. American Economic Review 107(1), 31–53 (2017)


Ely, J.C., Szydlowski, M.: Moving the goalposts. Journal of Political Economy 128(2), 468–506 (2020)


Farhadi, F., Teneketzis, D.: Dynamic information design: A simple problem on optimal sequential information disclosure. Available at SSRN 3554960 (2020)


Forges, F., Koessler, F.: Long persuasion games. Journal of Economic Theory 143(1), 1–35 (2008)


Gradwohl, R., Hahn, N., Hoefer, M., Smorodinsky, R.: Algorithms for persuasion with limited communication. In: Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA). pp. 637–652. SIAM (2021)


Honryo, T.: Dynamic persuasion. Journal of Economic Theory 178, 36–58 (2018)


Kamenica, E.: Bayesian persuasion and information design. Annual Review of Economics 11, 249 272 (2019)


Kamenica, E., Gentzkow, M.: Bayesian persuasion. American Economic Review 101(6), 2590–2615 (2011)


Kolotilin, A., Mylovanov, T., Zapechelnyuk, A., Li, M.: Persuasion of a privately informed receiver. Econometrica 85(6), 1949–1964 (2017)


Le Treust, M., Tomala, T.: Persuasion with limited communication capacity. Journal of Economic Theory 184, 104940 (2019)


Li, F., Norman, P.: On Bayesian persuasion with multiple senders. Economics Letters 170, 66–70 (2018)


Li, J., Zhou, J.: Blackwell’s informativeness ranking with uncertainty-averse preferences. Games and Economic Behavior 96, 18–29 (2016)


Meigs, E., Parise, F., Ozdaglar, A., Acemoglu, D.: Optimal dynamic information provision in traffic routing. arXiv preprint arXiv:2001.03232 (2020)


Nguyen, A., Tan, T.Y.: Bayesian persuasion with costly messages. Available at SSRN 3298275 (2019)


Su, S.T., Subramanian, V., Schoenebeck, G.: Bayesian persuasion in sequential trials. arXiv preprint arXiv:2110.09594 (2021) This paper is available on arxiv under CC 4.0 license. Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Authors: Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Problem Formulation 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 4.3 Multi-phase model and classical Bayesian persuasion and References 4.3 Multi-phase model and classical Bayesian persuasion Note that the pruned tree will potentially be unbalanced. Lemma 7. Given an N-phase trial M with binary-outcome experiments, if there exists a pruned N-phase trial model P run(M) such that the following two conditions hold, then the sender’s expected utility is given by an equivalent single-phase Bayesian persuasion model. Lemma 7. Given an N-phase trial M with binary-outcome experiments, if there exists a pruned N-phase trial model P run(M) such that the following two conditions hold, then the sender’s expected utility is given by an equivalent single-phase Bayesian persuasion model. For every non-trivial determined experiment, its sibling is either a trivial or a sender-designed experiment. There exists a least one sender-designed experiment in each (from root to leaf) experiment sequence of P run(M). For every non-trivial determined experiment, its sibling is either a trivial or a sender-designed experiment. For every non-trivial determined experiment, its sibling is either a trivial or a sender-designed experiment. For every non-trivial determined experiment, its sibling is either a trivial or a sender-designed experiment. There exists a least one sender-designed experiment in each (from root to leaf) experiment sequence of P run(M). There exists a least one sender-designed experiment in each (from root to leaf) experiment sequence of P run(M). There exists a least one sender-designed experiment in each (from root to leaf) experiment sequence of P run(M). References Au, P.H.: Dynamic information disclosure. The RAND Journal of Economics 46(4), 791–823 (2015) Basu, D.: Statistical information and likelihood [with discussion]. Sankhy¯a: The Indian Journal of Statistics, Series A pp. 1–71 (1975) Bergemann, D., Morris, S.: Information design: A unified perspective. Journal of Economic Literature 57(1), 44–95 (2019) Bizzotto, J., R¨udiger, J., Vigier, A.: Dynamic persuasion with outside information. American Economic Journal: Microeconomics 13(1), 179–94 (2021) Bizzotto, J., Vigier, A.: Can a better informed listener be easier to persuade? Economic Theory 72(3), 705–721 (2021) Blackwell, D.: Equivalent comparisons of experiments. The annals of mathematical statistics pp. 265–272 (1953) Dughmi, S., Kempe, D., Qiang, R.: Persuasion with limited communication. In: Proceedings of the 2016 ACM Conference on Economics and Computation. pp. 663–680 (2016) Dughmi, S., Xu, H.: Algorithmic Bayesian persuasion. SIAM Journal on Computing 50(3), 68–97 (2019) Ely, J.C.: Beeps. American Economic Review 107(1), 31–53 (2017) Ely, J.C., Szydlowski, M.: Moving the goalposts. Journal of Political Economy 128(2), 468–506 (2020) Farhadi, F., Teneketzis, D.: Dynamic information design: A simple problem on optimal sequential information disclosure. Available at SSRN 3554960 (2020) Forges, F., Koessler, F.: Long persuasion games. Journal of Economic Theory 143(1), 1–35 (2008) Gradwohl, R., Hahn, N., Hoefer, M., Smorodinsky, R.: Algorithms for persuasion with limited communication. In: Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA). pp. 637–652. SIAM (2021) Honryo, T.: Dynamic persuasion. Journal of Economic Theory 178, 36–58 (2018) Kamenica, E.: Bayesian persuasion and information design. Annual Review of Economics 11, 249 272 (2019) Kamenica, E., Gentzkow, M.: Bayesian persuasion. American Economic Review 101(6), 2590–2615 (2011) Kolotilin, A., Mylovanov, T., Zapechelnyuk, A., Li, M.: Persuasion of a privately informed receiver. Econometrica 85(6), 1949–1964 (2017) Le Treust, M., Tomala, T.: Persuasion with limited communication capacity. Journal of Economic Theory 184, 104940 (2019) Li, F., Norman, P.: On Bayesian persuasion with multiple senders. Economics Letters 170, 66–70 (2018) Li, J., Zhou, J.: Blackwell’s informativeness ranking with uncertainty-averse preferences. Games and Economic Behavior 96, 18–29 (2016) Meigs, E., Parise, F., Ozdaglar, A., Acemoglu, D.: Optimal dynamic information provision in traffic routing. arXiv preprint arXiv:2001.03232 (2020) Nguyen, A., Tan, T.Y.: Bayesian persuasion with costly messages. Available at SSRN 3298275 (2019) Su, S.T., Subramanian, V., Schoenebeck, G.: Bayesian persuasion in sequential trials. arXiv preprint arXiv:2110.09594 (2021) Au, P.H.: Dynamic information disclosure. The RAND Journal of Economics 46(4), 791–823 (2015) Au, P.H.: Dynamic information disclosure. The RAND Journal of Economics 46(4), 791–823 (2015) Basu, D.: Statistical information and likelihood [with discussion]. Sankhy¯a: The Indian Journal of Statistics, Series A pp. 1–71 (1975) Basu, D.: Statistical information and likelihood [with discussion]. Sankhy¯a: The Indian Journal of Statistics, Series A pp. 1–71 (1975) Bergemann, D., Morris, S.: Information design: A unified perspective. Journal of Economic Literature 57(1), 44–95 (2019) Bergemann, D., Morris, S.: Information design: A unified perspective. Journal of Economic Literature 57(1), 44–95 (2019) Bizzotto, J., R¨udiger, J., Vigier, A.: Dynamic persuasion with outside information. American Economic Journal: Microeconomics 13(1), 179–94 (2021) Bizzotto, J., R¨udiger, J., Vigier, A.: Dynamic persuasion with outside information. American Economic Journal: Microeconomics 13(1), 179–94 (2021) Bizzotto, J., Vigier, A.: Can a better informed listener be easier to persuade? Economic Theory 72(3), 705–721 (2021) Bizzotto, J., Vigier, A.: Can a better informed listener be easier to persuade? Economic Theory 72(3), 705–721 (2021) Blackwell, D.: Equivalent comparisons of experiments. The annals of mathematical statistics pp. 265–272 (1953) Blackwell, D.: Equivalent comparisons of experiments. The annals of mathematical statistics pp. 265–272 (1953) Dughmi, S., Kempe, D., Qiang, R.: Persuasion with limited communication. In: Proceedings of the 2016 ACM Conference on Economics and Computation. pp. 663–680 (2016) Dughmi, S., Kempe, D., Qiang, R.: Persuasion with limited communication. In: Proceedings of the 2016 ACM Conference on Economics and Computation. pp. 663–680 (2016) Dughmi, S., Xu, H.: Algorithmic Bayesian persuasion. SIAM Journal on Computing 50(3), 68–97 (2019) Dughmi, S., Xu, H.: Algorithmic Bayesian persuasion. SIAM Journal on Computing 50(3), 68–97 (2019) Ely, J.C.: Beeps. American Economic Review 107(1), 31–53 (2017) Ely, J.C.: Beeps. American Economic Review 107(1), 31–53 (2017) Ely, J.C., Szydlowski, M.: Moving the goalposts. Journal of Political Economy 128(2), 468–506 (2020) Ely, J.C., Szydlowski, M.: Moving the goalposts. Journal of Political Economy 128(2), 468–506 (2020) Farhadi, F., Teneketzis, D.: Dynamic information design: A simple problem on optimal sequential information disclosure. Available at SSRN 3554960 (2020) Farhadi, F., Teneketzis, D.: Dynamic information design: A simple problem on optimal sequential information disclosure. Available at SSRN 3554960 (2020) Forges, F., Koessler, F.: Long persuasion games. Journal of Economic Theory 143(1), 1–35 (2008) Forges, F., Koessler, F.: Long persuasion games. Journal of Economic Theory 143(1), 1–35 (2008) Gradwohl, R., Hahn, N., Hoefer, M., Smorodinsky, R.: Algorithms for persuasion with limited communication. In: Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA). pp. 637–652. SIAM (2021) Gradwohl, R., Hahn, N., Hoefer, M., Smorodinsky, R.: Algorithms for persuasion with limited communication. In: Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA). pp. 637–652. SIAM (2021) Honryo, T.: Dynamic persuasion. Journal of Economic Theory 178, 36–58 (2018) Honryo, T.: Dynamic persuasion. Journal of Economic Theory 178, 36–58 (2018) Kamenica, E.: Bayesian persuasion and information design. Annual Review of Economics 11, 249 272 (2019) Kamenica, E.: Bayesian persuasion and information design. Annual Review of Economics 11, 249 272 (2019) Kamenica, E., Gentzkow, M.: Bayesian persuasion. American Economic Review 101(6), 2590–2615 (2011) Kamenica, E., Gentzkow, M.: Bayesian persuasion. American Economic Review 101(6), 2590–2615 (2011) Kolotilin, A., Mylovanov, T., Zapechelnyuk, A., Li, M.: Persuasion of a privately informed receiver. Econometrica 85(6), 1949–1964 (2017) Kolotilin, A., Mylovanov, T., Zapechelnyuk, A., Li, M.: Persuasion of a privately informed receiver. Econometrica 85(6), 1949–1964 (2017) Le Treust, M., Tomala, T.: Persuasion with limited communication capacity. Journal of Economic Theory 184, 104940 (2019) Le Treust, M., Tomala, T.: Persuasion with limited communication capacity. Journal of Economic Theory 184, 104940 (2019) Li, F., Norman, P.: On Bayesian persuasion with multiple senders. Economics Letters 170, 66–70 (2018) Li, F., Norman, P.: On Bayesian persuasion with multiple senders. Economics Letters 170, 66–70 (2018) Li, J., Zhou, J.: Blackwell’s informativeness ranking with uncertainty-averse preferences. Games and Economic Behavior 96, 18–29 (2016) Li, J., Zhou, J.: Blackwell’s informativeness ranking with uncertainty-averse preferences. Games and Economic Behavior 96, 18–29 (2016) Meigs, E., Parise, F., Ozdaglar, A., Acemoglu, D.: Optimal dynamic information provision in traffic routing. arXiv preprint arXiv:2001.03232 (2020) Meigs, E., Parise, F., Ozdaglar, A., Acemoglu, D.: Optimal dynamic information provision in traffic routing. arXiv preprint arXiv:2001.03232 (2020) Nguyen, A., Tan, T.Y.: Bayesian persuasion with costly messages. Available at SSRN 3298275 (2019) Nguyen, A., Tan, T.Y.: Bayesian persuasion with costly messages. Available at SSRN 3298275 (2019) Su, S.T., Subramanian, V., Schoenebeck, G.: Bayesian persuasion in sequential trials. arXiv preprint arXiv:2110.09594 (2021) Su, S.T., Subramanian, V., Schoenebeck, G.: Bayesian persuasion in sequential trials. arXiv preprint arXiv:2110.09594 (2021) This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Generalizing Signaling Strategies in Multi-phase Trials

Authors:
(1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu);
(2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu);
(3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 4.2 Determined versus sender-designed experiments Given the model, the sender can manipulate the phase-K interim belief only when designing an experiment at phase K − 1. If an experiment at phase K − 1 is determined, then the phase-K interim belief is a function of interim belief at phase K − 1. Therefore, figuring out how these two types of experiments, determined and sender-designed experiments, will influence every given phase’s interim belief is the key to solving for the optimal signaling strategy. We start by noting that if the posterior belief at a leaf node is given, then the receiver’s action is determined - he will take the action with the highest posterior probability unless there is a tie, in which case he is indifferent and will follow the sender’s recommendation. Therefore, we can use backward iteration and the principle of optimality to determine the optimal signaling. We start by considering the last phase’s experiments when the sender can design them. Experiments in phase N − 1 In the second-last phase, results in Section 3.4 describe a sender-designed experiment’s role in the optimal signaling strategy: pick the strategy on the frontier of all persuasion-ratio curves. However, if the experiment is determined in the second-last phase, an additional constraint on the interim belief between the second-last phase and the last phase is enforced. That is to say, the set of (feasible) strategies will shrink. Fortunately, after enforcing the constraints, the process of searching for the optimal signaling strategy under a determined experiment is the same as the sender-designed experiment, i.e., pick the strategy in the frontier of all persuasion ratio curves. Therefore, at each possible branch of phase N − 1, we can plot an optimal persuasion ratio curve capturing the sender’s optimal signaling strategy at phase N − 1 and phase N. Non-binary Outcome Experiments When the experiments have non-binary outcomes, the same approach derived above works with an increased number of phases (if complexity is not an issue). For general non-binary experiments, see the proof of Lemma 6 in [23] for a detailed construction from non-binary to binary experiments. This paper is available on arxiv under CC 4.0 license. Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Authors: Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Problem Formulation 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 4.3 Multi-phase model and classical Bayesian persuasion and References 4.2 Determined versus sender-designed experiments Given the model, the sender can manipulate the phase-K interim belief only when designing an experiment at phase K − 1. If an experiment at phase K − 1 is determined, then the phase-K interim belief is a function of interim belief at phase K − 1. Therefore, figuring out how these two types of experiments, determined and sender-designed experiments, will influence every given phase’s interim belief is the key to solving for the optimal signaling strategy. We start by noting that if the posterior belief at a leaf node is given, then the receiver’s action is determined - he will take the action with the highest posterior probability unless there is a tie, in which case he is indifferent and will follow the sender’s recommendation. Therefore, we can use backward iteration and the principle of optimality to determine the optimal signaling. We start by considering the last phase’s experiments when the sender can design them. Experiments in phase N − 1 In the second-last phase, results in Section 3.4 describe a sender-designed experiment’s role in the optimal signaling strategy: pick the strategy on the frontier of all persuasion-ratio curves. However, if the experiment is determined in the second-last phase, an additional constraint on the interim belief between the second-last phase and the last phase is enforced. That is to say, the set of (feasible) strategies will shrink. Fortunately, after enforcing the constraints, the process of searching for the optimal signaling strategy under a determined experiment is the same as the sender-designed experiment, i.e., pick the strategy in the frontier of all persuasion ratio curves. Therefore, at each possible branch of phase N − 1, we can plot an optimal persuasion ratio curve capturing the sender’s optimal signaling strategy at phase N − 1 and phase N . Experiments in phase N − 1 N N N N Non-binary Outcome Experiments When the experiments have non-binary outcomes, the same approach derived above works with an increased number of phases (if complexity is not an issue). Non-binary Outcome Experiments For general non-binary experiments, see the proof of Lemma 6 in [23] for a detailed construction from non-binary to binary experiments. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Optimizing Signaling Strategies with Sender-Designed Experiments in Multi-phase Trials

Authors:
(1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu);
(2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu);
(3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 3.5 Comparison with classical Bayesian persuasion strategies Given the optimal signaling strategy derived in Lemma 5, one natural followup question is the quantification of the sender’s utility improvement obtained by adopting the optimal signaling strategy in comparison to using strategies structurally similar to the optimal strategies in classical Bayesian persuasion for a binary state of the world. Owing the page limit, we directly define a class of strategies structurally similar to the classical Bayesian persuasion strategy below and provide the justification in our online version [23]. Definition 4. With binary states of the world, a (binary-state) Bayesian persuasion (BBP) strategy is a strategy that “mixes two possible states in one signal and reveals the true state on the other signal”. This paper is available on arxiv under CC 4.0 license. Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Authors: Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Problem Formulation 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 4.3 Multi-phase model and classical Bayesian persuasion and References 3.5 Comparison with classical Bayesian persuasion strategies Given the optimal signaling strategy derived in Lemma 5, one natural followup question is the quantification of the sender’s utility improvement obtained by adopting the optimal signaling strategy in comparison to using strategies structurally similar to the optimal strategies in classical Bayesian persuasion for a binary state of the world. Owing the page limit, we directly define a class of strategies structurally similar to the classical Bayesian persuasion strategy below and provide the justification in our online version [23]. Definition 4. With binary states of the world, a (binary-state) Bayesian persuasion (BBP) strategy is a strategy that “mixes two possible states in one signal and reveals the true state on the other signal”. Definition 4. With binary states of the world, a (binary-state) Bayesian persuasion (BBP) strategy is a strategy that “mixes two possible states in one signal and reveals the true state on the other signal”. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

How Optimal Signaling Outperforms Classical Bayesian Strategies in Multi-Phase Trials

Authors:
(1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu);
(2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu);
(3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 3.4 Persuasion ratio and the optimal signaling structure Careful readers may notice that if we multiply the persuasion ratio with the prior, the value will be the (maximum) expected utility the sender can achieve from the given set of strategies. Since the sender’s expected utility is monotone increasing in the prior p regardless of which set of strategies the sender adopts, the persuasion ratio under a given prior can be viewed as the relative utility gain this set of strategies can offer to the sender. Hence, given a specific prior, if a set of strategies has a higher persuasion ratio with respect to another set of strategies, the sender should use a strategy in the former instead of the latter. According to this discussion, we can draw a persuasion ratio curve for each set of strategies as the prior is varied in [0, 1]. Abusing notation, we represent the persuasion ratio curve by P R(S). It may appear that an optimization needs to be carried out for each value of the prior. However, structural insights presented in the following two lemmas considerably simplify the analysis. Properties presented in Lemma 3 narrow down the space where the sender needs to search for the optimal signaling strategy. This allows us to depict persuasion ratio curves P R(S) for some basic strategies. On top of that, Lemma 4 provides a systematic approach to derive persuasion ratio curves for all types of strategies. Lemma 3. Given a type of strategy S and a prior p, there exists a (sender’s) optimal strategy S ∈ S which satisfies one of the following two conditions: At least one IC requirement of the constituent induced strategies is tight;


There is a signal that will be sent with probability 1 under S. Before discussing the simplifications that Lemma 3 yields in terms of the key properties for solving the problem, we give an intuitive outline of the proof of Lemma 3. When the IC requirements of the two induced strategies are not tight and both signals are sent with non-zero probability in a strategy S, the sender can increase her expected utility by slightly raising the probability of the signal with a higher persuasion ratio (and adjust the probability of the other signal to respect the prior) to form a strategy S+. The sender can keep doing this ‘slight’ modification of her strategies until either one of the IC conditions is satisfied or the signal is sent with probability one. Lemma 5. The persuasion ratio curve of the optimal signaling strategy P R∗ (p) is the upper envelope of the different types of strategies’ persuasion curves. Further, the optimal signaling strategy (under a given prior) is the strategy that reaches the frontier of the persuasion ratio curve (at that prior). For a two-phase trial or to solve the last two phases of a trial with more than two phases studied in Section 4, the following corollary can further simplify the sender’s optimization procedure. With Corollary 1, the Equation (3) in Lemma 4 reduces to a linear equation. Hence, the comparison in Lemma 5 and the computation in Lemma 4 can be reduced to a comparison of the (unique) corresponding IC strategies (if one exists) under the interim belief listed in Corollary1 for different types of strategies. This paper is available on arxiv under CC 4.0 license. Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Authors: Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Problem Formulation 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 4.3 Multi-phase model and classical Bayesian persuasion and References 3.4 Persuasion ratio and the optimal signaling structure Careful readers may notice that if we multiply the persuasion ratio with the prior, the value will be the (maximum) expected utility the sender can achieve from the given set of strategies. Since the sender’s expected utility is monotone increasing in the prior p regardless of which set of strategies the sender adopts, the persuasion ratio under a given prior can be viewed as the relative utility gain this set of strategies can offer to the sender. Hence, given a specific prior, if a set of strategies has a higher persuasion ratio with respect to another set of strategies, the sender should use a strategy in the former instead of the latter. According to this discussion, we can draw a persuasion ratio curve for each set of strategies as the prior is varied in [0, 1]. Abusing notation, we represent the persuasion ratio curve by P R(S). It may appear that an optimization needs to be carried out for each value of the prior. However, structural insights presented in the following two lemmas considerably simplify the analysis. Properties presented in Lemma 3 narrow down the space where the sender needs to search for the optimal signaling strategy. This allows us to depict persuasion ratio curves P R(S) for some basic strategies. On top of that, Lemma 4 provides a systematic approach to derive persuasion ratio curves for all types of strategies. Lemma 3. Given a type of strategy S and a prior p, there exists a (sender’s) optimal strategy S ∈ S which satisfies one of the following two conditions: Lemma 3. Given a type of strategy S and a prior p, there exists a (sender’s) optimal strategy S ∈ S which satisfies one of the following two conditions: At least one IC requirement of the constituent induced strategies is tight; There is a signal that will be sent with probability 1 under S. At least one IC requirement of the constituent induced strategies is tight; At least one IC requirement of the constituent induced strategies is tight; At least one IC requirement of the constituent induced strategies is tight; There is a signal that will be sent with probability 1 under S. There is a signal that will be sent with probability 1 under S. There is a signal that will be sent with probability 1 under S. Before discussing the simplifications that Lemma 3 yields in terms of the key properties for solving the problem, we give an intuitive outline of the proof of Lemma 3. When the IC requirements of the two induced strategies are not tight and both signals are sent with non-zero probability in a strategy S, the sender can increase her expected utility by slightly raising the probability of the signal with a higher persuasion ratio (and adjust the probability of the other signal to respect the prior) to form a strategy S+. The sender can keep doing this ‘slight’ modification of her strategies until either one of the IC conditions is satisfied or the signal is sent with probability one. Lemma 5. The persuasion ratio curve of the optimal signaling strategy P R∗ (p) is the upper envelope of the different types of strategies’ persuasion curves. Further, the optimal signaling strategy (under a given prior) is the strategy that reaches the frontier of the persuasion ratio curve (at that prior). Lemma 5. The persuasion ratio curve of the optimal signaling strategy P R∗ (p) is the upper envelope of the different types of strategies’ persuasion curves. Further, the optimal signaling strategy (under a given prior) is the strategy that reaches the frontier of the persuasion ratio curve (at that prior). For a two-phase trial or to solve the last two phases of a trial with more than two phases studied in Section 4, the following corollary can further simplify the sender’s optimization procedure. With Corollary 1, the Equation (3) in Lemma 4 reduces to a linear equation. Hence, the comparison in Lemma 5 and the computation in Lemma 4 can be reduced to a comparison of the (unique) corresponding IC strategies (if one exists) under the interim belief listed in Corollary1 for different types of strategies. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

How to Maximize Persuasion Ratios in Two-Phase Trials

Authors:
(1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu);
(2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu);
(3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 3.3 Constraints given by phase-II experiments By her choice of the experiment in phase I, the sender decides how to split the prior into the interim beliefs for the two experiments available in phase-II. The resulting interim-beliefs then lead to certain induced strategies at stage-II being applicable, i.e., incentive compatible (for the receiver). In other words, the probability pair (p1, p2) must make each (applied) induced strategy yield the maximum utility for the receiver. These requirements constrain the sender’s choice of (p1, p2), and the sender needs to account for the (reduced) choice while deciding the split of the prior. Table 1 summarizes the impact in terms of the parameters of the phase-I experiment via primary requirements on (p1, p2) driven by the incentive compatibility while using each class of induced strategies. Hereafter, when we use IC requirements without additional specification, we mean primary IC requirements. From the entries in the table, it is clear that the phase-II experiments (indirectly) limit the sender’s strategy selection where this limitation arises due the receiver’s IC requirements for each induced strategy (when that induced strategy is used). With this in mind, the sender’s experiment design in phase I, essentially, is to select between different combinations of these induced strategies such that each induced strategy satisfies the constraint listed in Table 1. Hence, we next seek to understand how these IC constraints collectively determine the sender’s strategy selection. To answer this, we first discuss the relationship between induced strategies, IC requirements, and the sender’s expected utility. taken, she would like to use the “most efficient”[4] pair of induced strategies to persuade the receiver[5]. To better understand the “efficiency” of induced strategies, we evaluate each induced strategy under a given phase-II experiment EX: This paper is available on arxiv under CC 4.0 license. Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Authors: Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Problem Formulation 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 4.3 Multi-phase model and classical Bayesian persuasion and References 3.3 Constraints given by phase-II experiments By her choice of the experiment in phase I, the sender decides how to split the prior into the interim beliefs for the two experiments available in phase-II. The resulting interim-beliefs then lead to certain induced strategies at stage-II being applicable, i.e., incentive compatible (for the receiver). In other words, the probability pair (p1, p2) must make each (applied) induced strategy yield the maximum utility for the receiver. These requirements constrain the sender’s choice of (p1, p2), and the sender needs to account for the (reduced) choice while deciding the split of the prior. Table 1 summarizes the impact in terms of the parameters of the phase-I experiment via primary requirements on (p1, p2) driven by the incentive compatibility while using each class of induced strategies. Hereafter, when we use IC requirements without additional specification, we mean primary IC requirements. From the entries in the table, it is clear that the phase-II experiments (indirectly) limit the sender’s strategy selection where this limitation arises due the receiver’s IC requirements for each induced strategy (when that induced strategy is used). With this in mind, the sender’s experiment design in phase I, essentially, is to select between different combinations of these induced strategies such that each induced strategy satisfies the constraint listed in Table 1. Hence, we next seek to understand how these IC constraints collectively determine the sender’s strategy selection. To answer this, we first discuss the relationship between induced strategies, IC requirements, and the sender’s expected utility. taken, she would like to use the “most efficient”[4] pair of induced strategies to persuade the receiver[5]. To better understand the “efficiency” of induced strategies, we evaluate each induced strategy under a given phase-II experiment EX: This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Understanding Incentive-Compatible Signaling in Two-Phase Trials

Authors:
(1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu);
(2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu);
(3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 3.2 Assumptions and induced strategies Next we detail the optimal signaling strategy in our two-phase trial setting with general binary-outcome experiments. To aid in the presentation and to avoid repetition, we make two assumptions without loss of generality and introduce several explanatory concepts before the analysis. Lemma 2. We can make the following two assumptions WLOG. The sender’s strategy consists of the following: choice of phase-I experiment parameters (p1, p2) and the persuasion strategies in phase-II for each outcome of the phase-I experiment. To understand better the choices available to the sender and her reasoning in determining her best strategy, we will study the possible persuasion strategies in phase-II; these will be called induced strategies to distinguish them from the entire strategy. Given the assumptions above on phase-II experiments, it’ll turn out we can directly rule out one class of induced strategies from the sender’s consideration. The other set of induced strategies will need careful assessment that we present next. This paper is available on arxiv under CC 4.0 license. [3] In terms of the Blackwell informativeness from [6]. Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Authors: Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Problem Formulation 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 4.3 Multi-phase model and classical Bayesian persuasion and References 3.2 Assumptions and induced strategies Next we detail the optimal signaling strategy in our two-phase trial setting with general binary-outcome experiments. To aid in the presentation and to avoid repetition, we make two assumptions without loss of generality and introduce several explanatory concepts before the analysis. Lemma 2. We can make the following two assumptions WLOG. Lemma 2. We can make the following two assumptions WLOG. The sender’s strategy consists of the following: choice of phase-I experiment parameters (p1, p2) and the persuasion strategies in phase-II for each outcome of the phase-I experiment. To understand better the choices available to the sender and her reasoning in determining her best strategy, we will study the possible persuasion strategies in phase-II; these will be called induced strategies to distinguish them from the entire strategy. Given the assumptions above on phase-II experiments, it’ll turn out we can directly rule out one class of induced strategies from the sender’s consideration. The other set of induced strategies will need careful assessment that we present next. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv [3] In terms of the Blackwell informativeness from [6].

Bayesian Persuasion in Sequential Trials: Assumptions and induced strategies

Authors:
(1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu);
(2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu);
(3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 3 Binary-outcome Experiments in Two-phase Trials In this section the sender’s optimization problem presented in (2) Section 2.1, is solved starting with the simplest non-trivial case. There are only two phases in the trial studied here, and from this we will develop more insight into how different types of experiments (determined versus sender-designed) influence the optimal signaling strategy of the sender. To be more specific, we will analyze how two determined experiments (in phase II) and one sender-designed experiment (in phase I) will impact the sender’s optimal signaling strategy. Before we present the general case, we discuss a subset class of two-phase trials that are similar to single-phase trials. In this class of two-phase trials, in one of the phase-II experiments, called a trivial experiment, the outcome distribution is independent of the true state. Trivial experiments [2], also called (Blackwell) non-informative experiments in some literature, are frequently used as benchmarks to compare the agents’ expected utility change under different signaling schemes/mechanisms, e.g., [22,20,21]. This two-phase model with a trivial experiment tries to capture real-world problems with one actual (and costly) experiment, e.g., clinical trials, venture capital investments, or space missions. Since the experiment is costly, a screening procedure is provided to decide whether it is worth conducting the experiment. We will then analyze the optimal signaling strategy in the general scenario, where both experiments in phase II are non-trivial. 3.1 Experiments with screenings We start by analyzing the sender’s optimal strategy (signaling structure) in a simple scenario where there is one non-trivial experiment conducted in phase II. The sender’s authority on choosing the probability pair (p1, p2) controls the screening process. To avoid any ambiguity, we first define what a trivial experiment is. When a trivial experiment (in phase II) is conducted, the posterior belief of the state stays the same as the interim belief derived in (1). When there exists a trivial experiment in the two phase-II trial options, then Lemma 1 states that the sender and the receiver’s expected utility under the optimal signaling strategy is the same as in the (single-phase) classical Bayesian persuasion problem. Lemma 1. When the state space is binary, both sender and receiver’s expected utilities are the same in the following two Bayesian persuasion schemes under each scheme’s optimal signaling strategy: Bayesian persuasion in a single-phase trial,


Bayesian persuasion in a two-phase trial with a sender-designed phase-I experiment and a trivial experiment in phase II. In the single-trial classical Bayesian persuasion setting, the optimal signaling strategy only mixes the two possible states in one outcome (e.g., when the prosecutor claims the suspect is guilty). On the other outcome, the sender reveals the true state with probability one (e.g., when the prosecutor says the suspect is innocent). When there is a trivial experiment in phase II, the other experiment (supposing that it will be conducted at outcome ωB) will be rendered defunct by the sender’s choice of experiments in phase I. This phenomenon occurs because the sender can always choose to reveal the true state when the non-trivial experiment is to be conducted, i.e., by setting P(θ1|EB) = 1 or P(θ2|EB) = 1; and the classical Bayesian persuasion strategy can be replicated. In essence, having a trivial experiment in the phase-II trial does not constrain the sender. This paper is available on arxiv under CC 4.0 license. Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Authors: Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Problem Formulation 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 4.3 Multi-phase model and classical Bayesian persuasion and References 3 Binary-outcome Experiments in Two-phase Trials In this section the sender’s optimization problem presented in (2) Section 2.1, is solved starting with the simplest non-trivial case. There are only two phases in the trial studied here, and from this we will develop more insight into how different types of experiments (determined versus sender-designed) influence the optimal signaling strategy of the sender. To be more specific, we will analyze how two determined experiments (in phase II) and one sender-designed experiment (in phase I) will impact the sender’s optimal signaling strategy. Before we present the general case, we discuss a subset class of two-phase trials that are similar to single-phase trials. In this class of two-phase trials, in one of the phase-II experiments, called a trivial experiment, the outcome distribution is independent of the true state. Trivial experiments [2], also called (Blackwell) non-informative experiments in some literature, are frequently used as benchmarks to compare the agents’ expected utility change under different signaling schemes/mechanisms, e.g., [22,20,21]. This two-phase model with a trivial experiment tries to capture real-world problems with one actual (and costly) experiment, e.g., clinical trials, venture capital investments, or space missions. Since the experiment is costly, a screening procedure is provided to decide whether it is worth conducting the experiment. We will then analyze the optimal signaling strategy in the general scenario, where both experiments in phase II are non-trivial. 3.1 Experiments with screenings We start by analyzing the sender’s optimal strategy (signaling structure) in a simple scenario where there is one non-trivial experiment conducted in phase II. The sender’s authority on choosing the probability pair (p1, p2) controls the screening process. To avoid any ambiguity, we first define what a trivial experiment is. When a trivial experiment (in phase II) is conducted, the posterior belief of the state stays the same as the interim belief derived in (1). When there exists a trivial experiment in the two phase-II trial options, then Lemma 1 states that the sender and the receiver’s expected utility under the optimal signaling strategy is the same as in the (single-phase) classical Bayesian persuasion problem. Lemma 1. When the state space is binary, both sender and receiver’s expected utilities are the same in the following two Bayesian persuasion schemes under each scheme’s optimal signaling strategy: Lemma 1. When the state space is binary, both sender and receiver’s expected utilities are the same in the following two Bayesian persuasion schemes under each scheme’s optimal signaling strategy: Bayesian persuasion in a single-phase trial, Bayesian persuasion in a two-phase trial with a sender-designed phase-I experiment and a trivial experiment in phase II. Bayesian persuasion in a single-phase trial, Bayesian persuasion in a single-phase trial, Bayesian persuasion in a single-phase trial, Bayesian persuasion in a two-phase trial with a sender-designed phase-I experiment and a trivial experiment in phase II. Bayesian persuasion in a two-phase trial with a sender-designed phase-I experiment and a trivial experiment in phase II. Bayesian persuasion in a two-phase trial with a sender-designed phase-I experiment and a trivial experiment in phase II. In the single-trial classical Bayesian persuasion setting, the optimal signaling strategy only mixes the two possible states in one outcome (e.g., when the prosecutor claims the suspect is guilty). On the other outcome, the sender reveals the true state with probability one (e.g., when the prosecutor says the suspect is innocent). When there is a trivial experiment in phase II, the other experiment (supposing that it will be conducted at outcome ωB) will be rendered defunct by the sender’s choice of experiments in phase I. This phenomenon occurs because the sender can always choose to reveal the true state when the non-trivial experiment is to be conducted, i.e., by setting P(θ1|EB) = 1 or P(θ2|EB) = 1; and the classical Bayesian persuasion strategy can be replicated. In essence, having a trivial experiment in the phase-II trial does not constrain the sender. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Analyzing Optimal Signaling with Binary-outcome Experiments in Two-phase Trials

Ontleed optimale sein met binêre uitkoms-eksperimente in twee-fase proewe

Análisis de la señalización óptima con experimentos de resultados binarios en ensayos de dos fases

تجزیه و تحلیل سیگنال دهی بهینه با آزمایش های باینری نتیجه در آزمایشات دو فازی

Analiza optimalnog signaliziranja s eksperimentima s binarnim ishodom u dvofaznim ispitivanjima

2段階試験におけるバイナリ結果実験による最適なシグナル伝達の分析

ოპტიმალური სიგნალიზაციის ანალიზი ორფაზიან ცდებში ორფაზიანი ექსპერიმენტებით

Екі фазалық сынақтардағы екілік нәтиже эксперименттерімен оңтайлы сигналды талдау

Go sekaseka Matshwao a Mabotse ka Diteko tša dipoelo tša Binary ka Ditekong tša Megato ye Mebedi

Анализ оптимальной сигнализации с помощью экспериментов с бинарным результатом в двухфазных испытаниях

Gusesengura Ibimenyetso Byiza hamwe na Binary-ibisubizo Ubushakashatsi Mubice bibiri

Анализа оптималне сигнализације са експериментима са бинарним исходом у двофазним испитивањима

دو فیز ٹرائلز میں بائنری نتائج کے تجربات کے ساتھ بہترین سگنلنگ کا تجزیہ کرنا

Authors:
(1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu);
(2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu);
(3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 2 Problem Formulation Before the receiver takes his action, a trial consisting of multiple phases will be run, and the outcome in each phase will be revealed to him. In each phase, one experiment will be conducted, which is chosen according to the outcomes in earlier phases. Hence, the experiment outcomes in earlier phases not only affect the interim belief but also influence the possible (sequence of) experiments that will be conducted afterward. In the most sender-friendly setup where the sender can choose any experiment in each phase without any constraints, the problem is equivalent to the classical Bayesian persuasion problem with an enlarged signal space. However, when some experiments are pre-determined conditional on a set of outcomes, the sender must take these constraints into account to design her optimal signaling structure. To present our results on the influence of multiple phases on the sender’s signaling strategy, we start with a model of two-phase trials with binary-outcome experiments in the rest of this section. We then analyze the optimal signaling strategy of this model in Section 3. After that, we will introduce the general model of multiple-phase trials with binary-outcome experiments and propose a systematic approach to analyze the optimal signaling structure in Section 4. This paper is available on arxiv under CC 4.0 license. Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Authors: Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Problem Formulation 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 4.3 Multi-phase model and classical Bayesian persuasion and References 2 Problem Formulation Before the receiver takes his action, a trial consisting of multiple phases will be run, and the outcome in each phase will be revealed to him. In each phase, one experiment will be conducted, which is chosen according to the outcomes in earlier phases. Hence, the experiment outcomes in earlier phases not only affect the interim belief but also influence the possible (sequence of) experiments that will be conducted afterward. In the most sender-friendly setup where the sender can choose any experiment in each phase without any constraints, the problem is equivalent to the classical Bayesian persuasion problem with an enlarged signal space. However, when some experiments are pre-determined conditional on a set of outcomes, the sender must take these constraints into account to design her optimal signaling structure. To present our results on the influence of multiple phases on the sender’s signaling strategy, we start with a model of two-phase trials with binary-outcome experiments in the rest of this section. We then analyze the optimal signaling strategy of this model in Section 3. After that, we will introduce the general model of multiple-phase trials with binary-outcome experiments and propose a systematic approach to analyze the optimal signaling structure in Section 4. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Formulating Optimal Signaling Strategies in Constrained Bayesian Persuasion Trials

Stories, News & Mentions about SENDERS

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