
on Microeconomics 
By:  Furkan Sezer; Hossein Khazaei; Ceyhun Eksin 
Abstract:  We consider linearquadratic Gaussian (LQG) games in which players have quadratic payoffs that depend on the players' actions and an unknown payoffrelevant state, and signals on the state that follow a Gaussian distribution conditional on the state realization. An information designer decides the fidelity of information revealed to the players in order to maximize the social welfare of the players or reduce the disagreement among players' actions. Leveraging the semidefiniteness of the information design problem, we derive analytical solutions for these objectives under specific LQG games. We show that full information disclosure maximizes social welfare when there is a common payoffrelevant state, when there is strategic substitutability in the actions of players, or when the signals are public. Numerical results show that as strategic substitution increases, the value of the information disclosure increases. When the objective is to induce conformity among players' actions, hiding information is optimal. Lastly, we consider the information design objective that is a weighted combination of social welfare and cohesiveness of players' actions. We obtain an interval for the weights where full information disclosure is optimal under public signals for games with strategic substitutability. Numerical solutions show that the actual interval where full information disclosure is optimal gets close to the analytical interval obtained as substitution increases. 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2102.13047&r=all 
By:  Franz Dietrich (Centre d'Economie de la Sorbonne, Paris School of Economics); Christian List (LudwigMaximilians Universität) 
Abstract:  Judgmentaggregation theory has always focused on the attainment of rational collective judgments. But so far, rationality has been understood in static terms: as "coherence" of judgments at a given time, understood as consistency, completeness, and/or deductive closure. By contrast, this paper discusses whether collective judgments can be dynamically rational, so that they change rationally in response to new information. Formally, a judgment aggregation rule is dynamically rational with respect to a given revision operator if, whenever all individuals revise their judgments in light of some information (a learnt proposition), then the new aggregate judgments are the old ones revised in light of this information, i.e., aggregation and revision commute. We prove a general impossibility theorem: if the propositions on the agenda are sufficiently interconnected, no judgment aggregation rule with standard properties is dynamically rational with respect to any revision operator satisfying some mild conditions (familiar from belief revision theory). Our theorem is the dynamicrationality analogue of some wellknown impossibility theorems for static rationality. We also exolore how dynamic rationality might be achieved by relaxing some of the conditions on the aggregation rule and/or the revision operator 
Keywords:  judgment aggregation; belief revision; static vs. dynamic rationality; premisebased rule 
JEL:  D70 D71 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:mse:cesdoc:21002&r=all 
By:  Florian Ederer (Cowles Foundation, Yale University); Weicheng Min (Yale Department of Economics) 
Abstract:  We consider a model of Bayesian persuasion in which the Receiver can detect lies with positive probability. We show that the Sender lies more when the lie detection probability increases. As long as the lie detection probability is suï¬€iciently small the Senderâ€™s and the Receiverâ€™s equilibrium payoï¬€s are unaï¬€ected by the lie detection technology because the Sender simply compensates by lying more. When the lie detection probability is suï¬€iciently high, the Senderâ€™s (Receiverâ€™s) equilibrium payoï¬€ decreases (increases) with the lie detection probability. 
Keywords:  Bayesian persuasion, Lying, Communication, Lie detection 
JEL:  D83 D82 K40 D72 
Date:  2021–01 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:2272&r=all 
By:  Andrew Jennings; Rida Laraki; Clemens Puppe; Estelle Varloot 
Abstract:  We provide novel simple representations of strategyproof voting rules when voters have unidimensional singlepeaked preferences (as well as multidimensional separable preferences). The analysis recovers, links and unifies existing results in the literature such as Moulin's classic characterization in terms of phantom voters and Barber\`a, Gul and Stacchetti's in terms of winning coalitions ("generalized median voter schemes"). First, we compare the computational properties of the various representations and show that the grading curve representation is superior in terms of computational complexity. Moreover, the new approach allows us to obtain new characterizations when strategyproofness is combined with other desirable properties such as anonymity, responsiveness, ordinality, participation, consistency, or proportionality. In the anonymous case, two methods are single out: the  well know  ordinal median and the  most recent  linear median. 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2102.11686&r=all 
By:  Komal Malik (Indian Statistical Institute, Delhi); Kolagani Paramahamsa (Indian Statistical Institute, Delhi) 
Abstract:  A seller is selling a pair of complementary goods to an agent. The agent consumes the goods only in a certain ratio and freely disposes of excess in either of the goods. The value of the bundle and the ratio are private information of the agent. In this twodimensional type space model, we characterize the incentive constraints and show that the optimal (expected revenuemaximizing) mechanism is a ratiodependent posted price mechanism for a class of distributions; that is, it has a diâ†µerent posted price for each ratio report. We identify additional sufficient conditions on the joint distribution for a posted price to be an optimal mechanism. We also show that the optimal mechanism is a posted price mechanism when the value and the ratio types are independently distributed. 
Keywords:  optimal mechanism, complementary goods, multidimensional private information, postedprice mechanism 
JEL:  D82 D40 D42 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:alo:isipdp:2101&r=all 
By:  You Zu; Krishnamurthy Iyer; Haifeng Xu 
Abstract:  We study a repeated persuasion setting between a sender and a receiver, where at each time $t$, the sender observes a payoffrelevant state drawn independently and identically from an unknown prior distribution, and shares state information with the receiver, who then myopically chooses an action. As in the standard setting, the sender seeks to persuade the receiver into choosing actions that are aligned with the sender's preference by selectively sharing information about the state. However, in contrast to the standard models, the sender does not know the prior, and has to persuade while gradually learning the prior on the fly. We study the sender's learning problem of making persuasive action recommendations to achieve low regret against the optimal persuasion mechanism with the knowledge of the prior distribution. Our main positive result is an algorithm that, with high probability, is persuasive across all rounds and achieves $O(\sqrt{T\log T})$ regret, where $T$ is the horizon length. The core philosophy behind the design of our algorithm is to leverage robustness against the sender's ignorance of the prior. Intuitively, at each time our algorithm maintains a set of candidate priors, and chooses a persuasion scheme that is simultaneously persuasive for all of them. To demonstrate the effectiveness of our algorithm, we further prove that no algorithm can achieve regret better than $\Omega(\sqrt{T})$, even if the persuasiveness requirements were significantly relaxed. Therefore, our algorithm achieves optimal regret for the sender's learning problem up to terms logarithmic in $T$. 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2102.10156&r=all 
By:  Hamid Aghadadashli; Georg Kirchsteiger; Patrick Legros 
Abstract:  The paper studies the effectiveness of communication in a twoplayer twosided asymmetric information context. Both players choose simultaneously between two actions, with action L leading to a lower payoff for the coplayer than action H. There are two types of players: Dtypes for whom L is dominant, and Ctypes for whom the optimal action is the same as the one chosen by the coplayer, with both player choosing H providing the Ctype a higher payoff than both players choosing L. Before the actions are chosen, each player can signal his/her intention to choose H. We consider three communication environments: No communication (NC), cheap talk (CT), and an environment with extrinsic communication costs (FC). According to standard theory the range of equilibrium payoffs of both types is the same in NC and CT, while for Ctypes the equilibrium payoff is highest in FC due to the Spence mechanism (Spence 1973). When we tested these predictions experimentally, the Ctype payoffs were the highest in CT. In this environment the average observed Ctype Payoff was even higher than the maximum equilibrium payoff. In CT about half of the Dtypes did not mimic the communication behavior of Ctypes, and hence even cheap talk revealed some information to the Ctypes. This indicates that half of the Dtypes were reluctant to make promises they would break. We introduce a theoretical model with promisekeepers. When the probability of an agent being promisekeeper is around 50%, the signaling rate will be higher in CT than in FC. On the other hand, for the same signal structure Ctypes choose more often H in the FC than in CT. These predictions are confirmed by the experimental results. Overall, the effect of the higher signalling rate in CT dominates: Together with presence of promisekeepers the higher signalling rate allows the Ctypes to coordinate more often on the « good » (H;H) outcome in CT, resulting in higher Ctype payoffs in CT than in FC. 
Keywords:  credible communication, asymmetric information, coordination 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:eca:wpaper:2013/319773&r=all 
By:  Marcus Roel (Beijing Normal University); Manuel Staab (AixMarseille University, CNRS, AMSE) 
Abstract:  In the spirit of Blackwell (1951), we analyze how two fundamental mistakes in information processingincorrect beliefs about the world and misperception of informationaffect the expected utility ranking of information experiments. We explore their individual and combined influence on welfare and provide necessary and sufficient conditions when mistakes alter and possibly reverse the ranking of information experiments. Both mistakes by themselves reduce welfare in a model where payoff relevant actions also generate informative signals. This is true for naive decisionmakers, unaware of any errors, as well as for sophisticated decisionmakers, who account for the possibility of mistakes. However, mistakes can interact in nonobvious ways and an agent might be better off suffering from both, rather than just one. We provide a characterization when such positive interactions are possible. Surprisingly, this holds true only for naive decisionmakers and thus naivete can be beneficial. We discuss implications for information acquisition and avoidance, welfareimproving belief manipulation, and policy interventions in general. 
Keywords:  ranking of experiments, information acquisition, misperception, confirmation bias, overconfidence, underconfidence 
JEL:  D03 D81 D83 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:aim:wpaimx:2108&r=all 
By:  Mira Frick (Cowles Foundation, Yale University); Ryota Iijima (Cowles Foundation, Yale University); Yuhta Ishii (Department of Economics at Pennsylvania State University) 
Abstract:  We study robust welfare comparisons of learning biases, i.e., deviations from correct Bayesian updating. Given a true signal distribution, we deem one bias more harmful than another if it yields lower objective expected payoï¬€s in all decision problems. We characterize this ranking in static (one signal) and dynamic (many signals) settings. While the static characterization compares posteriors signalbysignal, the dynamic characterization employs an â€œeï¬€iciency indexâ€ quantifying the speed of belief convergence. Our results yield welfarefounded quantiï¬ cations of the severity of welldocumented biases. Moreover, the static and dynamic rankings can conflict, and â€œsmallerâ€ biases can be worse in dynamic settings. 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:2274&r=all 
By:  Santiago Balseiro; Christian Kroer; Rachitesh Kumar 
Abstract:  The internet advertising market is a multibillion dollar industry, in which advertisers buy thousands of ad placements every day by repeatedly participating in auctions. In recent years, the industry has shifted to firstprice auctions as the preferred paradigm for selling advertising slots. Another important and ubiquitous feature of these auctions is the presence of campaign budgets, which specify the maximum amount the advertisers are willing to pay over a specified time period. In this paper, we present a new model to study the equilibrium bidding strategies in firstprice auctions for advertisers who satisfy budget constraints on average. Our model dispenses with the common, yet unrealistic assumption that advertisers' values are independent and instead assumes a contextual model in which advertisers determine their values using a common feature vector. We show the existence of a natural valuepacingbased BayesNash equilibrium under very mild assumptions, and study its structural properties. Furthermore, we generalize the existence result to standard auctions and prove a revenue equivalence showing that all standard auctions yield the same revenue even in the presence of budget constraints. 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2102.10476&r=all 
By:  Pawel Dziewulski (University of Sussex); John K.H. Quah (John Hopkins Univeristy) 
Abstract:  We formulate a set order on constraint sets C ? Rl which guarantee that argmin {?(x) : x ?C} increases in the product order as C increases in the set order, for all linear functions ?: Rl ?R. Using this result, we characterize the utility/production functions that lead to normal demand; we also show that this very same class of production functions have marginal costs that increase with factor prices. In the context of decisionmaking under uncertainty, our new set order leads to natural generalizations of first order stochastic dominance in multiprior models. 
Keywords:  parallelogram property, increasing differences, ambiguity, first order stochastic dominance, normal demand, marginal costs 
JEL:  C61 D21 D24 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:sus:susewp:0121&r=all 
By:  Elliot Lipnowski (Columbia University  Department of Economics); Doron Ravid (University of Chicago  Department of Economics) 
Abstract:  We study optimal testing to inform quarantine decisions for a population exhibiting a heterogeneous probability of carrying a pathogen. Because test supply is limited, the planner may choose to test a pooled sample, which contains the specimens of multiple individuals (Dorfman, 1943). We characterize the unique optimal allocation of tests. This allocation features assortative batching, whereby agents of differing infection risk are never jointly tested. Moreover, the planner tests only individuals whose prior quarantine decision is the most uncertain. Finally, individuals with higher infection risk are tested in smaller batches, because such tests minimize the informational externality of group testing. 
JEL:  D04 D61 I18 D62 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:bfi:wpaper:202085&r=all 
By:  Przemyslaw Rys; Maciej Sobolewski (European Commission â€“ JRC) 
Abstract:  The static model of two sided markets proposed by Rochet and Tirole analyses optimal pricing of a monopolistic platform at the equilibrium point. Their framework implicitly assumes that for each prices set by the platform, the equilibrium number of users on each side will be unique. However, under general conditions, the uniqueness of market equilibrium is not guaranteed. Optimal static prices do not ensure convergence to the preferred full market outcome, as platform may face failuretolaunch or failuretogrow problems. Hence, to study problems around multiplicity of equilibria, a different framework is required. We propose a dynamic model of monopolistic platform and demonstrate the effects of different dynamic pricing strategies for equilibrium selection and convergence. The main conclusion from the study is that emerging platform can reach the preferred equilibrium by using tariffs with subsidies for early stage users. We give examples of dynamically adjusting tariffs that minimize subsidies. Finally, the dynamic setting reveals a tradeoff between the platform profits and social welfare, related to the speed of user base growth. 
Keywords:  twosided markets, dynamic pricing, multiplicity of equilibria, dynamic system, online platforms 
JEL:  L12 C61 D42 
Date:  2020–12 
URL:  http://d.repec.org/n?u=RePEc:ipt:decwpa:202014&r=all 
By:  Semyon Malamud (Ecole Polytechnique Federale de Lausanne; Centre for Economic Policy Research (CEPR); Swiss Finance Institute); Anna Cieslak (Duke University  Fuqua School of Business; National Bureau of Economic Research (NBER)); Andreas Schrimpf (Bank for International Settlements (BIS)  Monetary and Economic Department) 
Abstract:  We study the general problem of optimal information design with continuous actions and continuous state space in arbitrary dimensions. First, we show that with a finite signal space, the optimal information design is always given by a partition. Second, we take the limit of an infinite signal space and characterize the solution in terms of a MongeKantorovich optimal transport problem with an endogenous information transport cost. We use our novel approach to: 1. Derive necessary and sufficient conditions for optimality based on Bregman divergences for nonconvex functions. 2. Compute exact bounds for the Hausdorff dimension of the support of an optimal policy. 3. Derive a nonlinear, secondorder partial differential equation whose solutions correspond to regular optimal policies. 
Keywords:  Bayesian Persuasion, Information Design, Signalling, Optimal Transport 
JEL:  D82 D83 E52 E58 E61 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:chf:rpseri:rp2115&r=all 
By:  Matthew Kovach 
Abstract:  Models of updating a set of priors either do not allow a decision maker to make inference about her priors (full bayesian updating or FB) or require an extreme degree of selection (maximum likelihood updating or ML). Therefore I characterize a general method for updating a set of priors, partial bayesian updating (PB), in which the decision maker (i) utilizes a threshold to determine whether a prior is likely enough, conditional on observed information, and then (ii) applies Bayes' rule to the sufficiently likely priors. I show that PB nests FB and ML and explore its behavioral properties. 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2102.11429&r=all 
By:  Dengji Zhao 
Abstract:  Mechanism design has traditionally assumed that the set of participants are fixed and known to the mechanism (the market owner) in advance. However, in practice, the market owner can only directly reach a small number of participants (her neighbours). Hence the owner often needs costly promotions to recruit more participants in order to get desirable outcomes such as social welfare or revenue maximization. In this paper, we propose to incentivize existing participants to invite their neighbours to attract more participants. However, they would not invite each other if they are competitors. We discuss how to utilize the conflict of interest between the participants to incentivize them to invite each other to form larger markets. We will highlight the early solutions and open the floor for discussing the fundamental open questions in the settings of auctions, coalitional games, matching and voting. 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2102.10347&r=all 
By:  Allan M Feldman (Department of Economics, Brown University); Ram Singh (Department of Economics, Delhi School of Economics) 
Abstract:  In many accident contexts, the accident harm depends on observable as well as unobservable dimensions of the precaution exercised by the parties involved. The observable dimensions are commonly referred to as the ‘care’ levels and the unobservable aspects as the ‘activity’ levels. In a seminal contribution, Shavell (1980) extended the scope of economic analysis of liability rules by providing a model that allows for the care as well as activity level choices. Subsequent works have used and extended Shavell’s model to predict outcomes under various liability rules and also to compare their efficiency properties. These works make several claims about the existence and efficiency of equilibria under different liability rules, without providing any formal proof. In this paper, we reexamine the prevalent claims in the literature using the standard model itself. Contrary to prevalent claims, we show that the standard negligence liability rules do not induce equilibrium for all the accident contexts admissible under the model. Under the standard model, even the ‘nofault’ rules can fail to induce a Nash equilibrium. In the absence of an equilibrium, it is not plausible to make a claim about efficiency of a rule perse or visavis other rules. We show that even with commonly used utility functions that meet all the requirements of the standard model, the social welfare function may not have a maximum. In many other situations fully compatible with the standard models, a maximum of the social welfare function is not discoverable by the first order conditions. Under the standard models, even individually optimum choices might not exist. We analyze the underlying problems with the standard models and offer some insights for future research on this subject. Key Words: Observable and Nonobservable Care, Activity Levels, Negligence Liability, Nofault Liability, Second Best, Nash equilibrium, Accident Loss, First Best. 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:cde:cdewps:315&r=all 
By:  Jidong Zhou (Cowles Foundation, Yale University) 
Abstract:  This paper studies how an improved information environment aï¬€ects consumer search and ï¬ rm competition. We ï¬ nd conditions for information improvement to have unambiguous impacts on search duration, price and consumer welfare. In many cases consumers beneï¬ t from information improvement regardless of how it aï¬€ects the market price, but there are also cases where information improvement raises price signiï¬ cantly so that consumers suï¬€er from it. Our model provides a uniï¬ ed way to consider the market implications of various types of information improvement such as search advertising, personalized recommendations, ï¬ ltering, and VR shopping technology. 
Keywords:  Consumer search, Price competition, Information improvement 
JEL:  D43 D83 L13 
Date:  2020–11 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:2264&r=all 
By:  JeanMarc Zogheib; Marc Bourreau 
Abstract:  We study the competition between a private firm and public firms on prices andinvestment in new infrastructures. While the private firm maximizes its profits,public firms maximize the sum of their profits and consumer surplus, subject to abudget constraint. We consider two scenarios of public intervention, with a nationalpublic firm and with local public firms. In a monopoly benchmark, we find that thenational public firm has the highest coverage and charges a uniform price allowingcrosssubsidies between highcost and lowcost areas. Moreover, the private firmcovers as much as local public firms. In a mixed duopoly, a stronger competitivepressure drives firms' prices up while it drives down (up) the national public (private)firm's coverage. 
Keywords:  public firms, investment, network industries, mixed duopoly. 
JEL:  D43 H44 L20 L33 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:drm:wpaper:20214&r=all 
By:  Alberto Bisin (NYU, NBER, and CEPR); Jared Rubin (Chapman University); Avner Seror (AixMarseille School of Economics); Thierry Verdier (PSE, Ecole des PontsParis Tech, PUCRio, and CEPR) 
Abstract:  Recent theories of the Long Divergence between Middle Eastern and Western European economies focus on Middle Eastern (over)reliance on religious legitimacy, use of slave soldiers, and persistence of restrictive proscriptions of religious (Islamic) law. These theories take as exogenous the cultural values that complement the prevailing institutions. As a result, they miss the role of cultural values in either supporting the persistence of or inducing change in the economic and institutional environment. In this paper, we address these issues by modeling the joint evolution of institutions and culture. In doing so, we place the various hypotheses of economic divergence into one, unifying framework. We highlight the role that cultural transmission plays in reinforcing institutional evolution toward either theocratic or secular states. We extend the model to shed light on political decentralization and technological change in the two regions. 
Keywords:  Long Divergence; cultural transmission; institutions; legitimacy; religion 
JEL:  O10 P16 P48 N34 N35 Z12 O33 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:chu:wpaper:2104&r=all 
By:  Eleonora Broccardo (University of Trento); Oliver D. Hart (Harvard University  Department of Economics; NBER); Luigi Zingales (University of Chicago  Booth School of Business; NBER) 
Abstract:  We study the relative effectiveness of exit (divestment and boycott) and voice (engagement) strategies in promoting socially desirable outcomes in companies. We show that in a competitive world exit is less effective than voice in pushing firms to act in a socially responsible manner. Furthermore, we demonstrate that individual incentives to join an exit strategy are not necessarily aligned with social incentives, whereas they are when welldiversified investors are allowed to express their voice. We discuss what social and legal considerations might sometimes make exit preferable to voice. 
JEL:  D02 D21 D23 D62 D64 H41 L21 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:bfi:wpaper:2020114&r=all 
By:  Simone Cerreiaâ€ Vioglio (UniversitÃ Bocconi  IGIER & Department of Decision Sciences); Lars Peter Hansen (University of Chicago  Department of Economics; NBER); Fabio Maccheroni (UniversitÃ Bocconi  IGIER & Department of Decision Sciences); Massimo Marinacci (UniversitÃ Bocconi  IGIER & Department of Decision Sciences) 
Abstract:  We use decision theory to confront uncertainty that is sufficiently broad to incorporate models as approximations. We presume the existence of a featured collection of what we call structured models that have explicit substantive motivations. The decision maker confronts uncertainty through the lens of these models, but also views these models as simplifications, and hence, as misspecified. We extend minmax analysis under model ambiguity to incorporate the uncertainty induced by acknowledging that the models used in decisionmaking are simplified approximations. Formally, we provide an axiomatic rationale for a decision criterion that incorporates model misspecification concerns. 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:bfi:wpaper:2020103&r=all 
By:  Geoffroy de Clippel; Rene Saran; Roberto Serrano 
Abstract:  In de Clippel, Saran, and Serrano (2019), it is shown that, perhaps surprisingly, the set of implementable social choice functions is essentially the same whether agents have bounded depth of reasoning or rational expectations. The picture is quite different when taking into account the possibility of small modeling mistakes. While continuous strict implementation becomes very demanding (Oury and Tercieux (2012) Ð OT), continuity in levelk implementation obtains essentially for free. A decomposition of the conditions implied by the OT implementation notion confirms that it is the use of equilibrium, and not continuity per se, that is responsible for the difference. 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:bro:econwp:2021002&r=all 