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Posted ContentDOI

Optimal Design for Social Learning

21 Sep 2015-Research Papers in Economics (Department of Economics, Columbia University)-
TL;DR: This paper studies the design of a recommender system for organizing social learning on a product and finds that fully transparent recommendations may become optimal if a (socially-benevolent) designer does not observe the agents’ costs of experimentation.
Abstract: This paper studies the design of a recommender system for organizing social learning on a product. To improve incentives for early experimentation, the optimal design trades off fully transparent social learning by over-recommending a product (or “spamming”) to a fraction of agents in the early phase of the product cycle. Under the optimal scheme, the designer spams very little about a product right after its release but gradually increases the frequency of spamming and stops it altogether when the product is deemed sufficiently unworthy of recommendation. The optimal recommender system involves randomly triggered spamming when recommendations are public—as is often the case for product ratings—and an information “blackout” followed by a burst of spamming when agents can choose when to check in for a recommendation. Fully transparent recommendations may become optimal if a (socially-benevolent) designer does not observe the agents’ costs of experimentation.

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Citations
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Journal ArticleDOI
TL;DR: This paper found that applicants with distinctively African-American names are 16% less likely to be accepted relative to identical hosts with White names on the same platform. But, their results suggest that only a subset of hosts discriminate.
Abstract: In an experiment on Airbnb, we find that applications from guests with distinctively African-American names are 16% less likely to be accepted relative to identical guests with distinctively White names. Discrimination occurs among landlords of all sizes, including small landlords sharing the property and larger landlords with multiple properties. It is most pronounced among hosts who have never had an African-American guest, suggesting only a subset of hosts discriminate. While rental markets have achieved significant reductions in discrimination in recent decades, our results suggest that Airbnb’s current design choices facilitate discrimination and raise the possibility of erasing some of these civil rights gains.

581 citations


Cites background from "Optimal Design for Social Learning"

  • ...Market design principles have generally focused on increasing the information flow and quality within a platform (Bolton et al 2013, Che and Horner 2014, Dai et al 2014, Fradkin et al 2014), but we highlight a situation in which platforms may be providing too much information....

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Proceedings ArticleDOI
25 Feb 2017
TL;DR: Evidence of bias is found that gender and race are significantly correlated with worker evaluations, which could harm the employment opportunities afforded to the workers on TaskRabbit and Fiverr.
Abstract: Online freelancing marketplaces have grown quickly in recent years. In theory, these sites offer workers the ability to earn money without the obligations and potential social biases associated with traditional employment frameworks. In this paper, we study whether two prominent online freelance marketplaces - TaskRabbit and Fiverr - are impacted by racial and gender bias. From these two platforms, we collect 13,500 worker profiles and gather information about workers' gender, race, customer reviews, ratings, and positions in search rankings. In both marketplaces, we find evidence of bias: we find that gender and race are significantly correlated with worker evaluations, which could harm the employment opportunities afforded to the workers. We hope that our study fuels more research on the presence and implications of discrimination in online environments.

237 citations

Posted Content
Aleksandrs Slivkins1
TL;DR: In this article, a more introductory, textbook-like treatment of multi-armed bandits is provided, with a self-contained, teachable technical introduction and a brief review of further developments; many of the chapters conclude with exercises.
Abstract: Multi-armed bandits a simple but very powerful framework for algorithms that make decisions over time under uncertainty. An enormous body of work has accumulated over the years, covered in several books and surveys. This book provides a more introductory, textbook-like treatment of the subject. Each chapter tackles a particular line of work, providing a self-contained, teachable technical introduction and a brief review of the further developments; many of the chapters conclude with exercises. The book is structured as follows. The first four chapters are on IID rewards, from the basic model to impossibility results to Bayesian priors to Lipschitz rewards. The next three chapters cover adversarial rewards, from the full-feedback version to adversarial bandits to extensions with linear rewards and combinatorially structured actions. Chapter 8 is on contextual bandits, a middle ground between IID and adversarial bandits in which the change in reward distributions is completely explained by observable contexts. The last three chapters cover connections to economics, from learning in repeated games to bandits with supply/budget constraints to exploration in the presence of incentives. The appendix provides sufficient background on concentration and KL-divergence. The chapters on "bandits with similarity information", "bandits with knapsacks" and "bandits and agents" can also be consumed as standalone surveys on the respective topics.

152 citations

Journal ArticleDOI
TL;DR: In this article, the authors characterize contests that maximize innovation when the designer chooses a prize-sharing scheme and a disclosure policy, and show that jointly modifying prize sharing and disclosure can increase innovation.
Abstract: We study contests for innovation with learning about the innovation’s feasibility and opponents’ outcomes. We characterize contests that maximize innovation when the designer chooses a prize-sharing scheme and a disclosure policy. A “public winner-takes-all” contest dominates public contests—where any success is immediately disclosed—with any other prize-sharing scheme as well as winner-takes-all contests with any other disclosure policy. Yet, jointly modifying prize sharing and disclosure can increase innovation. In a broad class of mechanisms, it is optimal to share the prize with disclosure following a certain number of successes; under simple conditions, a “hidden equal-sharing” contest is optimal.

108 citations

Journal ArticleDOI
TL;DR: In this article, the authors provide an economist's toolkit for designing online marketplaces, focusing on trust and reputation mechanisms, to facilitate transactions between strangers in the online marketplace.
Abstract: Executive SummaryOnline marketplaces have proliferated over the past decade, creating new markets where none existed. By reducing transaction costs, online marketplaces facilitate transactions that otherwise would not have occurred and enable easier entry of small sellers. One central challenge faced by designers of online marketplaces is how to build enough trust to facilitate transactions between strangers. This paper provides an economist’s tool kit for designing online marketplaces, focusing on trust and reputation mechanisms.

95 citations

References
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Journal ArticleDOI
TL;DR: In this article, the authors analyze a sequential decision model in which each decision maker looks at the decisions made by previous decision makers in taking her own decision, and they show that the decision rules that are chosen by optimizing individuals will be characterized by herd behavior.
Abstract: We analyze a sequential decision model in which each decision maker looks at the decisions made by previous decision makers in taking her own decision. This is rational for her because these other decision makers may have some information that is important for her. We then show that the decision rules that are chosen by optimizing individuals will be characterized by herd behavior; i.e., people will be doing what others are doing rather than using their information. We then show that the resulting equilibrium is inefficient.

5,956 citations


"Optimal Design for Social Learning" refers background in this paper

  • ...The first-best policy calls for the agents to start experimenting strictly before the true posterior rises to c, namely when p∗∗b c is reached....

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  • ...In standard models (for instance, Bikhchandani, Hirshleifer and Welsch, 1992; Banerjee, 1993), the sequence of agents take decisions myopically, ignoring the impact of their action on learning and future decisions and welfare....

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Posted Content
TL;DR: It is argued that localized conformity of behavior and the fragility of mass behaviors can be explained by informational cascades.
Abstract: An informational cascade occurs when it is optimal for an individual, having observed the actions of those ahead of him, to follow the behavior of the preceding individual without regard to his own information. We argue that localized conformity of behavior and the fragility of mass behaviors can be explained by informational cascades.

5,412 citations

Journal ArticleDOI
TL;DR: In this paper, the authors argue that localized conformity of behavior and the fragility of mass behaviors can be explained by informational cascades, where an individual, having observed the actions of those ahead of him, to follow the behavior of the preceding individual without regard to his own information.
Abstract: An informational cascade occurs when it is optimal for an individual, having observed the actions of those ahead of him, to follow the behavior of the preceding individual without regard to his own information. We argue that localized conformity of behavior and the fragility of mass behaviors can be explained by informational cascades.

4,731 citations

Book
18 Dec 1992
TL;DR: In this paper, an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions is given, as well as a concise introduction to two-controller, zero-sum differential games.
Abstract: This book is intended as an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions. The authors approach stochastic control problems by the method of dynamic programming. The text provides an introduction to dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. A new Chapter X gives an introduction to the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets. Chapter VI of the First Edition has been completely rewritten, to emphasize the relationships between logarithmic transformations and risk sensitivity. A new Chapter XI gives a concise introduction to two-controller, zero-sum differential games. Also covered are controlled Markov diffusions and viscosity solutions of Hamilton-Jacobi-Bellman equations. The authors have tried, through illustrative examples and selective material, to connect stochastic control theory with other mathematical areas (e.g. large deviations theory) and with applications to engineering, physics, management, and finance. In this Second Edition, new material on applications to mathematical finance has been added. Concise introductions to risk-sensitive control theory, nonlinear H-infinity control and differential games are also included.

3,885 citations


"Optimal Design for Social Learning" refers background or methods in this paper

  • ...To prove this claim, we invoke a verification theorem (see, for instance, Thm. 5.1 in Fleming and Soner, 2005)....

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  • ...The agents’ belief gt concerning the arrival of news is determined via (3):...

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  • ...Hence, α = α(l) := h− l k − lσ , (3) where h := l + α(k − l)....

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  • ...where (pt, gt) must follow the required laws of motion: (2) and (3), and μt = ρ + αt is the total experimentation rate and r is the discount rate of the designer....

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  • ...It is readily checked from (3) that the slope of the locus α t (l) is larger than the slope dα/dl along the locus (α t , l s t )s∈[0,mt], so that they cross only once....

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Book
01 Jan 1983
TL;DR: Theoretical Equivalence of Mayer, Lagrange, and Bolza Problems of Optimal Control, and the Necessary Conditions and Sufficient Conditions Convexity and Lower Semicontinuity.
Abstract: 1 Problems of Optimization-A General View.- 1.1 Classical Lagrange Problems of the Calculus of Variations.- 1.2 Classical Lagrange Problems with Constraints on the Derivatives.- 1.3 Classical Bolza Problems of the Calculus of Variations.- 1.4 Classical Problems Depending on Derivatives of Higher Order.- 1.5 Examples of Classical Problems of the Calculus of Variations.- 1.6 Remarks.- 1.7 The Mayer Problems of Optimal Control.- 1.8 Lagrange and Bolza Problems of Optimal Control.- 1.9 Theoretical Equivalence of Mayer, Lagrange, and Bolza Problems of Optimal Control. Problems of the Calculus of Variations as Problems of Optimal Control.- 1.10 Examples of Problems of Optimal Control.- 1.11 Exercises.- 1.12 The Mayer Problems in Terms of Orientor Fields.- 1.13 The Lagrange Problems of Control as Problems of the Calculus of Variations with Constraints on the Derivatives.- 1.14 Generalized Solutions.- Bibliographical Notes.- 2 The Classical Problems of the Calculus of Variations: Necessary Conditions and Sufficient Conditions Convexity and Lower Semicontinuity.- 2.1 Minima and Maxima for Lagrange Problems of the Calculus of Variations.- 2.2 Statement of Necessary Conditions.- 2.3 Necessary Conditions in Terms of Gateau Derivatives.- 2.4 Proofs of the Necessary Conditions and of Their Invariant Character.- 2.5 Jacobi's Necessary Condition.- 2.6 Smoothness Properties of Optimal Solutions.- 2.7 Proof of the Euler and DuBois-Reymond Conditions in the Unbounded Case.- 2.8 Proof of the Transversality Relations.- 2.9 The String Property and a Form of Jacobi's Necessary Condition.- 2.10 An Elementary Proof of Weierstrass's Necessary Condition.- 2.11 Classical Fields and Weierstrass's Sufficient Conditions.- 2.12 More Sufficient Conditions.- 2.13 Value Function and Further Sufficient Conditions.- 2.14 Uniform Convergence and Other Modes of Convergence.- 2.15 Semicontinuity of Functionals.- 2.16 Remarks on Convex Sets and Convex Real Valued Functions.- 2.17 A Lemma Concerning Convex Integrands.- 2.18 Convexity and Lower Semicontinuity: A Necessary and Sufficient Condition.- 2.19 Convexity as a Necessary Condition for Lower Semicontinuity.- 2.20 Statement of an Existence Theorem for Lagrange Problems of the Calculus of Variations.- Bibliographical Notes.- 3 Examples and Exercises on Classical Problems.- 3.1 An Introductory Example.- 3.2 Geodesics.- 3.3 Exercises.- 3.4 Fermat's Principle.- 3.5 The Ramsay Model of Economic Growth.- 3.6 Two Isoperimetric Problems.- 3.7 More Examples of Classical Problems.- 3.8 Miscellaneous Exercises.- 3.9 The Integral I = ?(x?2 ? x2)dt.- 3.10 The Integral I = ?xx?2dt.- 3.11 The Integral I = ?x?2(1 + x?)2dt.- 3.12 Brachistochrone, or Path of Quickest Descent.- 3.13 Surface of Revolution of Minimum Area.- 3.14 The Principles of Mechanics.- Bibliographical Notes.- 4 Statement of the Necessary Condition for Mayer Problems of Optimal Control.- 4.1 Some General Assumptions.- 4.2 The Necessary Condition for Mayer Problems of Optimal Control.- 4.3 Statement of an Existence Theorem for Mayer's Problems of Optimal Control.- 4.4 Examples of Transversality Relations for Mayer Problems.- 4.5 The Value Function.- 4.6 Sufficient Conditions.- 4.7 Appendix: Derivation of Some of the Classical Necessary Conditions of Section 2.1 from the Necessary Condition for Mayer Problems of Optimal Control.- 4.8 Appendix: Derivation of the Classical Necessary Condition for Isoperimetric Problems from the Necessary Condition for Mayer Problems of Optimal Control.- 4.9 Appendix: Derivation of the Classical Necessary Condition for Lagrange Problems of the Calculus of Variations with Differential Equations as Constraints.- Bibliographical Notes.- 5 Lagrange and Bolza Problems of Optimal Control and Other Problems.- 5.1 The Necessary Condition for Bolza and Lagrange Problems of Optimal Control.- 5.2 Derivation of Properties (P1?)-(P4?) from (P1)-(P4).- 5.3 Examples of Applications of the Necessary Conditions for Lagrange Problems of Optimal Control.- 5.4 The Value Function.- 5.5 Sufficient Conditions for the Bolza Problem.- Bibliographical Notes.- 6 Examples and Exercises on Optimal Control.- 6.1 Stabilization of a Material Point Moving on a Straight Line under a Limited External Force.- 6.2 Stabilization of a Material Point under an Elastic Force and a Limited External Force.- 6.3 Minimum Time Stabilization of a Reentry Vehicle.- 6.4 Soft Landing on the Moon.- 6.5 Three More Problems on the Stabilization of a Point Moving on a Straight Line.- 6.6 Exercises.- 6.7 Optimal Economic Growth.- 6.8 Two More Classical Problems.- 6.9 The Navigation Problem.- Bibliographical Notes.- 7 Proofs of the Necessary Condition for Control Problems and Related Topics.- 7.1 Description of the Problem of Optimization.- 7.2 Sketch of the Proofs.- 7.3 The First Proof.- 7.4 Second Proof of the Necessary Condition.- 7.5 Proof of Boltyanskii's Statements (4.6.iv-v).- Bibliographical Notes.- 8 The Implicit Function Theorem and the Elementary Closure Theorem.- 8.1 Remarks on Semicontinuous Functionals.- 8.2 The Implicit Function Theorem.- 8.3 Selection Theorems.- 8.4 Convexity, Caratheodory's Theorem, Extreme Points.- 8.5 Upper Semicontinuity Properties of Set Valued Functions.- 8.6 The Elementary Closure Theorem.- 8.7 Some Fatou-Like Lemmas.- 8.8 Lower Closure Theorems with Respect to Uniform Convergence.- Bibliographical Notes.- 9 Existence Theorems: The Bounded, or Elementary, Case.- 9.1 Ascoli's Theorem.- 9.2 Filippov's Existence Theorem for Mayer Problems of Optimal Control.- 9.3 Filippov's Existence Theorem for Lagrange and Bolza Problems of Optimal Control.- 9.4 Elimination of the Hypothesis that A Is Compact in Filippov's Theorem for Mayer Problems.- 9.5 Elimination of the Hypothesis that A Is Compact in Filippov's Theorem for Lagrange and Bolza Problems.- 9.6 Examples.- Bibliographical Notes.- 10 Closure and Lower Closure Theorems under Weak Convergence.- 10.1 The Banach-Saks-Mazur Theorem.- 10.2 Absolute Integrability and Related Concepts.- 10.3 An Equivalence Theorem.- 10.4 A Few Remarks on Growth Conditions.- 10.5 The Growth Property (?) Implies Property (Q).- 10.6 Closure Theorems for Orientor Fields Based on Weak Convergence.- 10.7 Lower Closure Theorems for Orientor Fields Based on Weak Convergence.- 10.8 Lower Semicontinuity in the Topology of Weak Convergence.- 10.9 Necessary and Sufficient Conditions for Lower Closure.- Bibliographical Notes.- 11 Existence Theorems: Weak Convergence and Growth Conditions.- 11.1 Existence Theorems for Orientor Fields and Extended Problems.- 112 Elimination of the Hypothesis that A Is Bounded in Theorems (11.1. i-iv).- 11.3 Examples.- 11.4 Existence Theorems for Problems of Optimal Control with Unbounded Strategies.- 11.5 Elimination of the Hypothesis that A Is Bounded in Theorems (11.4.i-v).- 11.6 Examples.- 11.7 Counterexamples.- Bibliographical Notes.- 12 Existence Theorems: The Case of an Exceptional Set of No Growth.- 12.1 The Case of No Growth at the Points of a Slender Set. Lower Closure Theorems..- 12.2 Existence Theorems for Extended Free Problems with an Exceptional Slender Set.- 12.3 Existence Theorems for Problems of Optimal Control with an Exceptional Slender Set.- 12.4 Examples.- 12.5 Counterexamples.- Bibliographical Notes.- 13 Existence Theorems: The Use of Lipschitz and Tempered Growth Conditions.- 13.1 An Existence Theorem under Condition (D).- 13.2 Conditions of the F, G, and H Types Each Implying Property (D) and Weak Property (Q).- 13.3 Examples.- Bibliographical Notes.- 14 Existence Theorems: Problems of Slow Growth.- 14.1 Parametric Curves and Integrals.- 14.2 Transformation of Nonparametric into Parametric Integrals.- 14.3 Existence Theorems for (Nonparametric) Problems of Slow Growth.- 14.4 Examples.- Bibliographical Notes.- 15 Existence Theorems: The Use of Mere Pointwise Convergence on the Trajectories.- 15.1 The Helly Theorem.- 15.2 Closure Theorems with Components Converging Only Pointwise.- 15.3 Existence Theorems for Extended Problems Based on Pointwise Convergence.- 15.4 Existence Theorems for Problems of Optimal Control Based on Pointwise Convergence.- 15.5 Exercises.- Bibliographical Notes.- 16 Existence Theorems: Problems with No Convexity Assumptions.- 16.1 Lyapunov Type Theorems.- 16.2 The Neustadt Theorem for Mayer Problems with Bounded Controls.- 16.3 The Bang-Bang Theorem.- 16.4 The Neustadt Theorem for Lagrange and Bolza Problems with Bounded Controls.- 16.5 The Case of Unbounded Controls.- 16.6 Examples for the Unbounded Case.- 16.7 Problems of the Calculus of Variations without Convexity Assumptions.- Bibliographical Notes.- 17 Duality and Upper Semicontinuity of Set Valued Functions.- 17.1 Convex Functions on a Set.- 17.2 The Function T(x z).- 17.3 Seminormality.- 17.4 Criteria for Property (Q).- 17.5 A Characterization of Property (Q) for the Sets $$\tilde Q$$(t, x) in Terms of Seminormality.- 17.6 Duality and Another Characterization of Property (Q) in Terms of Duality.- 17.7 Characterization of Optimal Solutions in Terms of Duality.- 17.8 Property (Q) as an Extension of Maximal Monotonicity.- Bibliographical Notes.- 18 Approximation of Usual and of Generalized Solutions.- 18.1 The Gronwall Lemma.- 18.2 Approximation of AC Solutions by Means of C1 Solutions.- 18.3 The Brouwer Fixed Point Theorem.- 18.4 Further Results Concerning the Approximation of AC Trajectories by Means of C1 Trajectories.- 18.5 The Infimum for AC Solutions Can Be Lower than the One for C1 Solutions.- 18.6 Approximation of Generalized Solutions by Means of Usual Solutions.- 18.7 The Infimum for Generalized Solutions Can Be Lower than the One for Usual Solutions.- Bibliographical Notes.- Author Index.

2,371 citations


"Optimal Design for Social Learning" refers methods in this paper

  • ...A solution exists by the Filippov-Cesari theorem (Cesari, 1983)....

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