scholarly journals Prophet Inequalities for Bayesian Persuasion

2020 ◽  
Author(s):  
Niklas Hahn ◽  
Martin Hoefer ◽  
Rann Smorodinsky
Keyword(s):  
Expected Utility ◽  
Design Problem ◽  
Information Structure ◽  
A Priori ◽  
Status Quo ◽  
Structure Design ◽  
Approximation Factor ◽  
Multiple Receivers ◽  
Finite Approximation

We study an information-structure design problem (i.e., a Bayesian persuasion problem) in an online scenario. Inspired by the classic gambler's problem, consider a set of candidates who arrive sequentially and are evaluated by one agent (the sender). This agent learns the value from hiring the candidate to herself as well as the value to another agent, the receiver. The sender provides a signal to the receiver who, in turn, makes an irrevocable decision on whether or not to hire the candidate. A-priori, for each agent the distribution of valuation is independent across candidates but may not be identical. We design good online signaling schemes for the sender. To assess the performance, we compare the expected utility to that of an optimal offline scheme by a prophet sender who knows all candidate realizations in advance. We show an optimal prophet inequality for online Bayesian persuasion, with a 1/2-approximation when the instance satisfies a "satisfactory-status-quo" assumption. Without this assumption, there are instances without any finite approximation factor. We extend the results to combinatorial domains and obtain prophet inequalities for matching with multiple hires and multiple receivers.

scholarly journals Private Bayesian Persuasion with Sequential Games

2020 ◽  
Vol 34 (02) ◽  
pp. 1886-1893
Author(s):  
Andrea Celli ◽  
Stefano Coniglio ◽  
Nicola Gatti
Keyword(s):  
Information Structure ◽  
Imperfect Information ◽  
Probability Distributions ◽  
A Priori ◽  
Continuous Optimization ◽  
Structure Design ◽  
Ellipsoid Method ◽  
Additional Information ◽  
Multiple Receivers ◽  
Ex Ante

We study an information-structure design problem (a.k.a. a persuasion problem) with a single sender and multiple receivers with actions of a priori unknown types, independently drawn from action-specific marginal probability distributions. As in the standard Bayesian persuasion model, the sender has access to additional information regarding the action types, which she can exploit when committing to a (noisy) signaling scheme through which she sends a private signal to each receiver. The novelty of our model is in considering the much more expressive case in which the receivers interact in a sequential game with imperfect information, with utilities depending on the game outcome and the realized action types. After formalizing the notions of ex ante and ex interim persuasiveness (which differ by the time at which the receivers commit to following the sender's signaling scheme), we investigate the continuous optimization problem of computing a signaling scheme which maximizes the sender's expected revenue. We show that computing an optimal ex ante persuasive signaling scheme is NP-hard when there are three or more receivers. Instead, in contrast with previous hardness results for ex interim persuasion, we show that, for games with two receivers, an optimal ex ante persuasive signaling scheme can be computed in polynomial time thanks to the novel algorithm we propose, based on the ellipsoid method.

scholarly journals Hierarchical Matching and Regression with Application to Photometric Redshift Estimation

2016 ◽  
Vol 12 (S325) ◽  
pp. 145-155
Author(s):  
Fionn Murtagh
Keyword(s):  
Information Structure ◽  
Data Analytics ◽  
A Priori ◽  
Sloan Digital Sky Survey ◽  
Photometric Redshifts ◽  
Merging Galaxies ◽  
Photometric Redshift ◽  
Sky Survey ◽  
Wide Range ◽  
Regression Problems

AbstractThis work emphasizes that heterogeneity, diversity, discontinuity, and discreteness in data is to be exploited in classification and regression problems. A global a priori model may not be desirable. For data analytics in cosmology, this is motivated by the variety of cosmological objects such as elliptical, spiral, active, and merging galaxies at a wide range of redshifts. Our aim is matching and similarity-based analytics that takes account of discrete relationships in the data. The information structure of the data is represented by a hierarchy or tree where the branch structure, rather than just the proximity, is important. The representation is related to p-adic number theory. The clustering or binning of the data values, related to the precision of the measurements, has a central role in this methodology. If used for regression, our approach is a method of cluster-wise regression, generalizing nearest neighbour regression. Both to exemplify this analytics approach, and to demonstrate computational benefits, we address the well-known photometric redshift or ‘photo-z’ problem, seeking to match Sloan Digital Sky Survey (SDSS) spectroscopic and photometric redshifts.

A Scheme for Numerical Representation of Graph Structures in Engineering Design

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
David F. Wyatt ◽  
David C. Wynn ◽  
P. John Clarkson
Keyword(s):  
Engineering Design ◽  
Design Problem ◽  
Structure Design ◽  
Numerical Representation ◽  
Graph Structure ◽  
Numerical Techniques ◽  
Mathematical Properties ◽  
Conversion Algorithm ◽  
Graph Structures ◽  
Improve Access

Graph structures are fundamental in many aspects of design. This paper discusses a way to improve access to design spaces of graph structures, by converting graph structures into numerical values and vice versa. Mathematical properties of such conversions are described, and those that are desirable are identified. A candidate conversion algorithm, Indexed Stacked Blocks, is proposed. Its use and benefits are illustrated through an example graph-structure design problem. The example demonstrates that such conversions allow design spaces of graph structures to be visualized, sampled, and evaluated. In principle, they also allow other powerful numerical techniques to be applied to the design of graph-structure-based systems.

scholarly journals Educação e ideologia: em busca da crítica emancipatória

2018 ◽  
Vol 10 (21) ◽  
pp. 70
Author(s):  
Helenice Pereira Sardenberg ◽  
Igor Baptista De Oliveira Medeiros
Keyword(s):  
A Priori ◽  
Status Quo

O presente artigo busca discutir o papel da escola, na contemporaneidade, sem perder de vista a ideologia que permeia os processos e práticas no campo da educação. Entende-se que esta ideologia, focada numa perspectiva de mercado, incita a manutenção do status quo de pequena parcela da população, além de inviabilizar a emancipação da maioria, na medida em que exclui para “incluir perversamente”. Neste sentido, discute-se não apenas o capital cultural da elite dominante, mas, também, o processo de socialização, não menos importante no contexto escolar, forjado por uma visão capitalista a priori excludente.

scholarly journals Information and Communication in Organizations

2019 ◽  
Vol 109 ◽  
pp. 545-549 ◽  
Author(s):  
Inga Deimen ◽  
DezsÖ Szalay
Keyword(s):  
Decision Making ◽  
Decision Maker ◽  
Design Problem ◽  
Information Structure ◽  
Information Design ◽  
Communication In Organizations ◽  
Information And Communication ◽  
Optimal Information

We study a constrained information design problem in an organization. A designer chooses the information structure. A sender with preferences different from the decision-maker observes and processes the information before he communicates with the decision-maker. Information shapes conflicts within the organization: the optimal information structure essentially eliminates conflicts and serves as a substitute to the allocation of decision-making authority in the organization.

Stakeholder Fairness Under an Induced ‘Veil of Ignorance'

2019 ◽  
Vol 10 (1) ◽  
pp. 65-81 ◽  
Author(s):  
Sumit Sarkar ◽  
Soumyakanti Chakraborty
Keyword(s):  
Discrete Choice ◽  
Expected Utility ◽  
John Rawls ◽  
Status Quo ◽  
Veil Of Ignorance ◽  
Maximin Principle ◽  
Nash Demand Game ◽  
The Veil ◽  
John Harsanyi ◽  
Simultaneous Move

John Rawls introduced the ‘veil of ignorance' in social contract theory to bring about a common conception of justice, and hypothesized that it will enable rational individuals to choose distributive shares on basis of ‘maximin' principle. R. E. Freeman conceptualised stakeholder fairness using the Rawlsian ‘veil of ignorance'. In contrast to Rawls' theory, John Harsanyi postulated that rational individuals behind the ‘veil of ignorance' will choose allocation to maximise expected utility. This article investigates how subjects choose allocations behind the ‘veil of ignorance,' in a laboratory experiment, and interprets the findings in light of stakeholder fairness. The ‘veil of ignorance' was induced on randomly paired and mutually anonymous subjects, who were asked to choose allocations in a simultaneous move discrete choice Nash demand game. Both ‘maximin' principle and expected utility maximisation was found to be used by the subjects. Choice of allocations where no one is worse off vis-à-vis status quo was salient. This is consistent with Freeman's Principle of Governance.

scholarly journals On the Fair Division of a Random Object

2021 ◽  
Author(s):  
Anna Bogomolnaia ◽  
Hervé Moulin ◽  
Fedor Sandomirskiy
Keyword(s):  
Probability Distribution ◽  
Behavioral Economics ◽  
Decision Analysis ◽  
Expected Utility ◽  
Design Problem ◽  
Fair Division ◽  
Statistical Information ◽  
Equal Division ◽  
Fair Share ◽  
The Mean

Ann likes oranges much more than apples; Bob likes apples much more than oranges. Tomorrow they will receive one fruit that will be an orange or an apple with equal probability. Giving one half to each agent is fair for each realization of the fruit. However, agreeing that whatever fruit appears will go to the agent who likes it more gives a higher expected utility to each agent and is fair in the average sense: in expectation, each agent prefers the allocation to the equal division of the fruit; that is, the agent gets a fair share. We turn this familiar observation into an economic design problem: upon drawing a random object (the fruit), we learn the realized utility of each agent and can compare it to the mean of the agent’s distribution of utilities; no other statistical information about the distribution is available. We fully characterize the division rules using only this sparse information in the most efficient possible way while giving everyone a fair share. Although the probability distribution of individual utilities is arbitrary and mostly unknown to the manager, these rules perform in the same range as the best rule when the manager has full access to this distribution. This paper was accepted by Ilia Tsetlin, behavioral economics and decision analysis.

scholarly journals Costly verification in collective decisions

2020 ◽  
Vol 15 (3) ◽  
pp. 923-954
Author(s):  
Albin Erlanson ◽  
Andreas Kleiner
Keyword(s):  
Expected Utility ◽  
Status Quo ◽  
Voting Rule ◽  
Collective Decisions ◽  
Monetary Transfers ◽  
The Status ◽  
Privately Held

We study how a principal should optimally choose between implementing a new policy and maintaining the status quo when information relevant for the decision is privately held by agents. Agents are strategic in revealing their information; the principal cannot use monetary transfers to elicit this information, but can verify an agent's claim at a cost. We characterize the mechanism that maximizes the expected utility of the principal. This mechanism can be implemented as a cardinal voting rule, in which agents can either cast a baseline vote, indicating only whether they are in favor of the new policy, or make specific claims about their type. The principal gives more weight to specific claims and verifies a claim whenever it is decisive.

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