nep-mic New Economics Papers
on Microeconomics
Issue of 2021‒03‒01
23 papers chosen by
Jing-Yuan Chiou
National Taipei University

  1. Social Welfare Maximization and Conformism via Information Design in Linear-Quadratic-Gaussian Games By Furkan Sezer; Hossein Khazaei; Ceyhun Eksin
  2. Dynamically rational judgmentaggregation By Franz Dietrich; Christian List
  3. Bayesian Persuasion with Lie Detection By Florian Ederer; Weicheng Min
  4. New Characterizations of Strategy-Proofness under Single-Peakedness By Andrew Jennings; Rida Laraki; Clemens Puppe; Estelle Varloot
  5. Selling two complementary goods By Komal Malik; Kolagani Paramahamsa
  6. Learning to Persuade on the Fly: Robustness Against Ignorance By You Zu; Krishnamurthy Iyer; Haifeng Xu
  7. Cheap Talk is not Cheap: Free versus Costly Communication By Hamid Aghadadashli; Georg Kirchsteiger; Patrick Legros
  8. The benefits of being misinformed By Marcus Roel; Manuel Staab
  9. Welfare Comparisons for Biased Learning By Mira Frick; Ryota Iijima; Yuhta Ishii
  10. Contextual First-Price Auctions with Budgets By Santiago Balseiro; Christian Kroer; Rachitesh Kumar
  11. Comparative statics with linear objectives: normal demand, monotone marginal costs, and ranking multi-prior beliefs By Pawel Dziewulski; John K.-H. Quah
  12. Pooled Testing for Quarantine Decisions By Elliot Lipnowski; Doron Ravid
  13. Two-sided platforms: dynamic pricing and multiple equilibria By Przemyslaw Rys; Maciej Sobolewski
  14. Optimal Transport of Information By Semyon Malamud; Anna Cieslak; Andreas Schrimpf
  15. Ambiguity and Partial Bayesian Updating By Matthew Kovach
  16. Mechanism Design Powered by Social Interactions By Dengji Zhao
  17. Equilibria under Liability Rules: How the standard claims fall apart By Allan M Feldman; Ram Singh
  18. Improved Information in Search Markets By Jidong Zhou
  19. Public vs. Private Investments In Network Industries By Jean-Marc Zogheib; Marc Bourreau
  20. Culture, Institutions & the Long Divergence By Alberto Bisin; Jared Rubin; Avner Seror; Thierry Verdier
  21. Exit vs. Voice By Eleonora Broccardo; Oliver D. Hart; Luigi Zingales
  22. Making Decisions under Model Misspecification By Simone Cerreia†Vioglio; Lars Peter Hansen; Fabio Maccheroni; Massimo Marinacci
  23. Continuous Level-k Mechanism Design By Geoffroy de Clippel; Rene Saran; Roberto Serrano

  1. By: Furkan Sezer; Hossein Khazaei; Ceyhun Eksin
    Abstract: We consider linear-quadratic Gaussian (LQG) games in which players have quadratic payoffs that depend on the players' actions and an unknown payoff-relevant 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 semi-definiteness 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 payoff-relevant 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
  2. By: Franz Dietrich (Centre d'Economie de la Sorbonne, Paris School of Economics); Christian List (Ludwig-Maximilians Universität)
    Abstract: Judgment-aggregation 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 dynamic-rationality analogue of some well-known 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; premise-based rule
    JEL: D70 D71
    Date: 2021–02
  3. 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 sufficiently small the Sender’s and the Receiver’s equilibrium payoffs are unaffected by the lie detection technology because the Sender simply compensates by lying more. When the lie detection probability is sufficiently high, the Sender’s (Receiver’s) equilibrium payoff decreases (increases) with the lie detection probability.
    Keywords: Bayesian persuasion, Lying, Communication, Lie detection
    JEL: D83 D82 K40 D72
    Date: 2021–01
  4. By: Andrew Jennings; Rida Laraki; Clemens Puppe; Estelle Varloot
    Abstract: We provide novel simple representations of strategy-proof voting rules when voters have uni-dimensional single-peaked preferences (as well as multi-dimensional 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 strategy-proofness 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
  5. 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 two-dimensional type space model, we characterize the incentive constraints and show that the optimal (expected revenue-maximizing) mechanism is a ratio-dependent posted price mechanism for a class of distributions; that is, it has a di↵erent 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, posted-price mechanism
    JEL: D82 D40 D42
    Date: 2021–02
  6. 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 payoff-relevant 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
  7. By: Hamid Aghadadashli; Georg Kirchsteiger; Patrick Legros
    Abstract: The paper studies the effectiveness of communication in a two-player two-sided asymmetric information context. Both players choose simultaneously between two actions, with action L leading to a lower payoff for the co-player than action H. There are two types of players: D-types for whom L is dominant, and C-types for whom the optimal action is the same as the one chosen by the co-player, with both player choosing H providing the C-type 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 C-types the equilibrium payoff is highest in FC due to the Spence mechanism (Spence 1973). When we tested these predictions experimentally, the C-type payoffs were the highest in CT. In this environment the average observed C-type Payoff was even higher than the maximum equilibrium payoff. In CT about half of the D-types did not mimic the communication behavior of C-types, and hence even cheap talk revealed some information to the C-types. This indicates that half of the D-types were reluctant to make promises they would break. We introduce a theoretical model with promise-keepers. When the probability of an agent being promise-keeper is around 50%, the signaling rate will be higher in CT than in FC. On the other hand, for the same signal structure C-types 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 promise-keepers the higher signalling rate allows the C-types to coordinate more often on the « good » (H;H) outcome in CT, resulting in higher C-type payoffs in CT than in FC.
    Keywords: credible communication, asymmetric information, coordination
    Date: 2021–02
  8. By: Marcus Roel (Beijing Normal University); Manuel Staab (Aix-Marseille University, CNRS, AMSE)
    Abstract: In the spirit of Blackwell (1951), we analyze how two fundamental mistakes in information processing-incorrect beliefs about the world and misperception of information-affect 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 decision-makers, who account for the possibility of mistakes. However, mistakes can interact in non-obvious 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 decision-makers and thus naivete can be beneficial. We discuss implications for information acquisition and avoidance, welfare-improving 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
  9. 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 payoffs in all decision problems. We characterize this ranking in static (one signal) and dynamic (many signals) settings. While the static characterization compares posteriors signal-by-signal, the dynamic characterization employs an “efficiency index†quantifying the speed of belief convergence. Our results yield welfare-founded quantiï¬ cations of the severity of well-documented biases. Moreover, the static and dynamic rankings can conflict, and “smaller†biases can be worse in dynamic settings.
    Date: 2021–02
  10. By: Santiago Balseiro; Christian Kroer; Rachitesh Kumar
    Abstract: The internet advertising market is a multi-billion 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 first-price 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 first-price 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 value-pacing-based Bayes-Nash 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
  11. 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 decision-making under uncertainty, our new set order leads to natural generalizations of first order stochastic dominance in multi-prior models.
    Keywords: parallelogram property, increasing differences, ambiguity, first order stochastic dominance, normal demand, marginal costs
    JEL: C61 D21 D24
    Date: 2021–02
  12. 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
  13. By: Przemyslaw Rys; Maciej Sobolewski (European Commission – 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 failure-to-launch or failure-to-grow 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 trade-off between the platform profits and social welfare, related to the speed of user base growth.
    Keywords: two-sided markets, dynamic pricing, multiplicity of equilibria, dynamic system, online platforms
    JEL: L12 C61 D42
    Date: 2020–12
  14. 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 Monge-Kantorovich 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 non-convex functions. 2. Compute exact bounds for the Hausdorff dimension of the support of an optimal policy. 3. Derive a non-linear, second-order 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
  15. 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
  16. 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
  17. 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 ‘no-fault’ 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 per-se or vis-a-vis 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 Non-observable Care, Activity Levels, Negligence Liability, No-fault Liability, Second Best, Nash equilibrium, Accident Loss, First Best.
    Date: 2021–02
  18. By: Jidong Zhou (Cowles Foundation, Yale University)
    Abstract: This paper studies how an improved information environment affects 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 affects the market price, but there are also cases where information improvement raises price signiï¬ cantly so that consumers suffer 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
  19. By: Jean-Marc 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 allowingcross-subsidies between high-cost and low-cost 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
  20. By: Alberto Bisin (NYU, NBER, and CEPR); Jared Rubin (Chapman University); Avner Seror (Aix-Marseille School of Economics); Thierry Verdier (PSE, Ecole des Ponts-Paris Tech, PUC-Rio, 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
  21. 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 well-diversified 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
  22. By: Simone Cerreia†Vioglio (Università Bocconi - IGIER & Department of Decision Sciences); Lars Peter Hansen (University of Chicago - Department of Economics; NBER); Fabio Maccheroni (Università Bocconi - IGIER & Department of Decision Sciences); Massimo Marinacci (Università 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 min-max analysis under model ambiguity to incorporate the uncertainty induced by acknowledging that the models used in decision-making are simplified approximations. Formally, we provide an axiomatic rationale for a decision criterion that incorporates model misspecification concerns.
    Date: 2020
  23. 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 level-k 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

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