nep-mic New Economics Papers
on Microeconomics
Issue of 2021‒07‒26
twenty papers chosen by
Jing-Yuan Chiou
National Taipei University

  1. Price caps as welfare-enhancing coopetition By Patrick Rey; Jean Tirole
  2. Behavior-Based Price Discrimination with endogenous data collection and strategic customer targeting By Antoine Dubus
  3. The Optimality of Upgrade Pricing By Dirk Bergemann; Alessandro Bonatti; Andreas Haupt; Alex Smolin
  4. Monotone Comparative Statics in the Calvert-Wittman Model By Francisco Rodr\'iguez; Eduardo Zambrano
  5. Collective Progress: Dynamics of Exit Waves By Doruk Cetemen; Can Urgun; Leeat Yariv
  6. On the Foundations of Competitive Search Equilibrium with and without Market Makers By Albrecht, James; Cai, Xiaoming; Gautier, Pieter A.; Vroman, Susan
  7. Optimal portfolio under ambiguous ambiguity By Makarov, Dmitry
  8. Centralized Matching with Incomplete Information By Marcelo Ariel Fernandez; Kirill Rudov; Leeat Yariv
  9. Data Sharing Markets By Mohammad Rasouli; Michael I. Jordan
  10. Decision making with dynamic probabilistic forecasts By Peter Tankov; Laura Tinsi
  11. Information Design in Large Games By Frederic Koessler; Marco Scarsini; Tristan Tomala
  12. Graphical Economies with Resale By Gabriel P. Andrade; Rafael Frongillo; Elliot Gorokhovsky; Sharadha Srinivasan
  13. Order Symmetry: A New Fairness Criterion for Assignment Mechanisms By Freeman, Rupert; Pritchard, Geoffrey; Wilson, Mark
  14. Risk aversion and uniqueness of equilibrium in economies with two goods and HARA preferences By Andrea Loi; Stefano Matta
  15. Equilibrium with non-convex preferences: some examples By Cuong Le Van; Ngoc-Sang Pham
  16. Rationalization, Quantal Response Equilibrium, and Robust Outcomes in Large Populations By Shuige Liu; Fabio Maccheroni
  17. Auction Design with Data-Driven Misspecifications By Philippe Jehiel; Konrad Mierendorff
  18. A Smoothed Impossibility Theorem on Condorcet Criterion and Participation By Lirong Xia
  19. Keeping the Agents in the Dark: Private Disclosures in Competing Mechanisms By Andrea Attar; Eloisa Campioni; Thomas Mariotti; Alessandro Pavan
  20. Unifying Classical and Bayesian Revealed Preference By Kunal Pattanayak; Vikram Krishnamurthy

  1. By: Patrick Rey (TSE - Toulouse School of Economics - UT1 - Université Toulouse 1 Capitole - Université Fédérale Toulouse Midi-Pyrénées - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Jean Tirole (TSE - Toulouse School of Economics - UT1 - Université Toulouse 1 Capitole - Université Fédérale Toulouse Midi-Pyrénées - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)
    Abstract: The paper analyzes the impact of price caps agreed upon by industry participants. Price caps, like mergers, allow firms to solve Cournot's multiple marginalization problem; but unlike mergers, they do not stifle price competition in case of substitutes or facilitate foreclosure in case of complements. The paper first demonstrates this for non-repeated interaction and general demand and cost functions. It then shows that allowing price caps has no impact on investment and entry in case of substitutes. Under more restrictive assumptions, the paper finally generalizes the insights to repeated price interaction, analyzing coordinated effects when goods are not necessarily substitutes.
    Keywords: Coopetition,Joint marketing agreements,Foreclosure,Mergers,Complements and substitutes,Tacit collusion,Information-light regulation,Price caps
    Date: 2019–12
  2. By: Antoine Dubus (Télécom ParisTech)
    Abstract: This article analyzes behavior-based price discrimination in a two-period competition framework where firms endogenously collect consumer data and strategically target past customers. When firms strategically target customers: (i) they price-discriminate high valuation customers; (ii) they charge a homogeneous price to low valuation customers, even when they have precise information on them. Strategic targeting questions the main classical results of the literature: in a symmetric equilibrium firms do not compete for customer information acquisition and there is no consumer poaching. Sufficiently asymmetric data collection costs can restore previous results of the literature, and we discuss their implications for firms' data strategies and competition in digital markets.
    Keywords: Behavior-based price discrimination,Strategic Targeting,Data collection
    Date: 2021–06–24
  3. By: Dirk Bergemann; Alessandro Bonatti; Andreas Haupt; Alex Smolin
    Abstract: We consider a multiproduct monopoly pricing model. We provide sufficient conditions under which the optimal mechanism can be implemented via upgrade pricing -- a menu of product bundles that are nested in the strong set order. Our approach exploits duality methods to identify conditions on the distribution of consumer types under which (a) each product is purchased by the same set of buyers as under separate monopoly pricing (though the transfers can be different), and (b) these sets are nested. We exhibit two distinct sets of sufficient conditions. The first set of conditions is given by a weak version of monotonicity of types and virtual values, while maintaining a regularity assumption, i.e., that the product-by-product revenue curves are single-peaked. The second set of conditions establishes the optimality of upgrade pricing for type spaces with monotone marginal rates of substitution (MRS) -- the relative preference ratios for any two products are monotone across types. The monotone MRS condition allows us to relax the earlier regularity assumption. Under both sets of conditions, we fully characterize the product bundles and prices that form the optimal upgrade pricing menu. Finally, we show that, if the consumer's types are monotone, the seller can equivalently post a vector of single-item prices: upgrade pricing and separate pricing are equivalent.
    Date: 2021–07
  4. By: Francisco Rodr\'iguez; Eduardo Zambrano
    Abstract: In this paper, we show that when policy-motivated parties can commit to a particular platform during a uni-dimensional electoral contest where valence issues do not arise there must be a positive association between the policies preferred by candidates and the policies adopted in expectation in the lowest and the highest equilibria of the electoral contest. We also show that this need not be so if the parties cannot commit to a particular policy. The implication is that evidence of a negative relationship between enacted and preferred policies is suggestive of parties that hold positions from which they would like to move from yet are unable to do so.
    Date: 2021–07
  5. By: Doruk Cetemen; Can Urgun; Leeat Yariv
    Abstract: We study a model of collective search by teams. Discoveries beget discoveries and correlated search results are governed by a Brownian path. Search results' variation at any point---the search scope---is jointly controlled. Agents individually choose when to cease search and implement their best discovery. We characterize equilibrium and optimal policies. Search scope is constant and independent of search outcomes as long as no member leaves. It declines after departures. A simple drawdown stopping boundary governs each agent’s search termination. We show the emergence of endogenous exit waves, whereby possibly heterogeneous agents cease search all at once.
    JEL: C73 D81 D83 O35
    Date: 2021–07
  6. By: Albrecht, James (Georgetown University); Cai, Xiaoming (Peking University); Gautier, Pieter A. (Vrije Universiteit Amsterdam); Vroman, Susan (Georgetown University)
    Abstract: The literature offers two foundations for competitive search equilibrium, a Nash approach and a market-maker approach. When each buyer visits only one seller (or each worker makes only one job application), the two approaches are equivalent. However, when each buyer visits multiple sellers, this equivalence can break down. Our paper analyzes competitive search equilibrium with simultaneous search using the two approaches. We consider four cases defined by (i) the surplus structure (are the goods substitutes or complements?) and (ii) the mechanism space (do sellers post fees or prices?). With fees, the two approaches yield the same constrained efficient equilibrium. With prices, the equilibrium allocation is the same using both approaches if the goods are complements, but is not constrained efficient. In the case in which only prices are posted and the goods are substitutes, the equilibrium allocations from the two approaches are different.
    Keywords: multiple applications, competitive search, market makers, efficiency
    JEL: C78 D44 D83
    Date: 2021–06
  7. By: Makarov, Dmitry
    Abstract: A prominent approach to modelling ambiguity about stock return distribution is to assume that investors have multiple priors about the distribution and these priors are distributed according to a certain second-order distribution. Realistically, investors may also have multiple priors about the second-order distribution, thus allowing for ambiguous ambiguity. Despite a long history of debates about this idea (Reichenbach [1949], Savage [1954]), there seems to be no formal analysis of investment behavior in the presence of this feature. We develop a tractable portfolio choice framework incorporating ambiguous ambiguity, characterize analytically the optimal portfolio, and examine its properties.
    Keywords: ambiguous ambiguity, portfolio choice, smooth ambiguity, third-order probabilities
    JEL: D81 G11
    Date: 2020–06
  8. By: Marcelo Ariel Fernandez; Kirill Rudov; Leeat Yariv
    Abstract: We study the impacts of incomplete information on centralized one-to-one matching markets. We focus on the commonly used Deferred Acceptance mechanism (Gale and Shapley, 1962). We show that many complete-information results are fragile to a small infusion of uncertainty about others' preferences.
    Date: 2021–07
  9. By: Mohammad Rasouli; Michael I. Jordan
    Abstract: With the growing use of distributed machine learning techniques, there is a growing need for data markets that allows agents to share data with each other. Nevertheless data has unique features that separates it from other commodities including replicability, cost of sharing, and ability to distort. We study a setup where each agent can be both buyer and seller of data. For this setup, we consider two cases: bilateral data exchange (trading data with data) and unilateral data exchange (trading data with money). We model bilateral sharing as a network formation game and show the existence of strongly stable outcome under the top agents property by allowing limited complementarity. We propose ordered match algorithm which can find the stable outcome in O(N^2) (N is the number of agents). For the unilateral sharing, under the assumption of additive cost structure, we construct competitive prices that can implement any social welfare maximizing outcome. Finally for this setup when agents have private information, we propose mixed-VCG mechanism which uses zero cost data distortion of data sharing with its isolated impact to achieve budget balance while truthfully implementing socially optimal outcomes to the exact level of budget imbalance of standard VCG mechanisms. Mixed-VCG uses data distortions as data money for this purpose. We further relax zero cost data distortion assumption by proposing distorted-mixed-VCG. We also extend our model and results to data sharing via incremental inquiries and differential privacy costs.
    Date: 2021–07
  10. By: Peter Tankov; Laura Tinsi
    Abstract: We consider a sequential decision making process, such as renewable energy trading or electrical production scheduling, whose outcome depends on the future realization of a random factor, such as a meteorological variable. We assume that the decision maker disposes of a dynamically updated probabilistic forecast (predictive distribution) of the random factor. We propose several stochastic models for the evolution of the probabilistic forecast, and show how these models may be calibrated from ensemble forecasts, commonly provided by weather centers. We then show how these stochastic models can be used to determine optimal decision making strategies depending on the forecast updates. Applications to wind energy trading are given.
    Date: 2021–06
  11. By: Frederic Koessler; Marco Scarsini; Tristan Tomala
    Abstract: We define the notion of Bayes correlated Wardrop equilibrium for general nonatomic games with anonymous players and incomplete information. Bayes correlated Wardrop equilibria describe the set of equilibrium outcomes when a mediator, such as a traffic information system, provides information to the players. We relate this notion to Bayes Wardrop equilibrium. Then, we provide conditions -- existence of a convex potential and complete information -- under which mediation does not improve equilibrium outcomes. We then study full implementation and, finally, information design in anonymous games with a finite set of players, when the number of players tends to infinity.
    Date: 2021–07
  12. By: Gabriel P. Andrade; Rafael Frongillo; Elliot Gorokhovsky; Sharadha Srinivasan
    Abstract: Kakade, Kearns, and Ortiz (KKO) introduce a graph-theoretic generalization of the classic Arrow--Debreu (AD) exchange economy. Despite its appeal as a networked version of AD, we argue that the KKO model is too local, in the sense that goods cannot travel more than one hop through the network. We introduce an alternative model in which agents may purchase goods on credit in order to resell them. In contrast to KKO, our model allows for long-range trade, and yields equilibria in more settings than KKO, including sparse endowments. Our model smoothly interpolates between the KKO and AD equilibrium concepts: we recover KKO when the resale capacity is zero, and recover AD when it is sufficiently large. We give general equilibrium existence results, and an auction-based algorithm to compute approximate equilibria when agent utilities satisfy the weak gross-substitutes property.
    Date: 2021–06
  13. By: Freeman, Rupert; Pritchard, Geoffrey; Wilson, Mark
    Abstract: We introduce a new fairness criterion, order symmetry, for assignment mechanisms that match n objects to n agents with ordinal preferences over the objects. An assignment mechanism is order symmetric with respect to some probability measure over preference profiles if every agent is equally likely to receive their favorite object, every agent is equally likely to receive their second favorite, and so on. When associated with a sufficiently symmetric probability measure, order symmetry is a relaxation of anonymity that, crucially, can be satisfied by discrete assignment mechanisms. Furthermore, it can be achieved without sacrificing other desirable axiomatic properties satisfied by existing mechanisms. In particular, we show that it can be achieved in conjunction with strategyproofness and ex post efficiency via the top trading cycles mechanism (but not serial dictatorship). We additionally design a novel mechanism that is both order symmetric and ordinally efficient. The practical utility of order symmetry is substantiated by simulations on Impartial Culture and Mallows-distributed preferences for four common assignment mechanisms.
    Date: 2021–07–22
  14. By: Andrea Loi; Stefano Matta
    Abstract: We study the connection between risk aversion, number of consumers and uniqueness of equilibrium. We consider an economy with two goods and $c$ impatience types, where each type has additive separable preferences with HARA Bernoulli utility function, $u_H(x):=\frac{\gamma}{1-\gamma}(b+\frac{a}{\gamma}x)^{1-\gamma}$. We show that if $\gamma\in (1, \frac{c}{c-1}]$, the equilibrium is unique. Moreover, the methods used, involving Newton's symmetric polynomials and Descartes' rule of signs, enable us to offer new sufficient conditions for uniqueness in a closed-form expression highlighting the role played by endowments, patience and specific HARA parameters. Finally new necessary and sufficient conditions in ensuring uniqueness are derived for the particular case of CRRA Bernoulli utility functions with $\gamma =3$.
    Date: 2021–07
  15. By: Cuong Le Van (IPAG Business School, CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - ENPC - École des Ponts ParisTech - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique); Ngoc-Sang Pham (Métis Lab EM Normandie - EM Normandie - École de Management de Normandie, EM Normandie - École de Management de Normandie)
    Abstract: We study the existence of equilibrium when agents' preferences may not be convex. For some specific utility functions, we provide a necessary and sufficient condition under which there exists an equilibrium. The standard approach cannot be directly applied to our examples because the demand correspondence of some agents is neither single valued nor convex valued.
    Keywords: general equilibrium.,Non-convex preferences
    Date: 2021–03–23
  16. By: Shuige Liu; Fabio Maccheroni
    Abstract: This paper provides a robust epistemic foundation for predicting and implementing collective actions when only the proportions that take specific actions in the population matter. We apply $\Delta$-rationalizability to analyze strategic sophistication entailed in (structural) quantal response equilibrium (QRE); the former is called $\Delta(p)$-rationalization to emphasize the only requirement on first-order beliefs is that they should be consistent with the transparent knowledge of the distributions of errors in the population. We show that each QRE is a $\Delta(p)$-rationalizable outcome. We also give conditions under which the converse also holds, and prove that the condition is almost never satisfied in generic games. It implies that QRE may be too demanding as a predictor in general, and $\Delta(p)$-rationalizable outcomes can be a robust benchmark to start from.
    Date: 2021–06
  17. By: Philippe Jehiel; Konrad Mierendorff
    Abstract: We consider auction environments in which at the time of the auction bidders observe signals about their ex-post value. We introduce a model of novice bidders who do not know know the joint distribution of signals and instead build a statistical model relating others' bids to their own ex post value from the data sets accessible from past similar auctions. Crucially, we assume that only ex post values and bids are accessible while signals observed by bidders in past auctions remain private. We consider steady-states in such environments, and importantly we allow for correlation in the signal distribution. We first observe that data-driven bidders may behave suboptimally in classical auctions such as the second-price or first-price auctions whenever there are correlations. Allowing for a mix of rational (or experienced) and data-driven (novice) bidders results in inefficiencies in such auctions, and we show the inefficiency extends to all auction-like mechanisms in which bidders are restricted to submit one-dimensional (real-valued) bids.
    Date: 2021–07
  18. By: Lirong Xia
    Abstract: In 1988, Moulin proved an insightful and surprising impossibility theorem that reveals a fundamental incompatibility between two commonly-studied axioms of voting: no resolute voting rule (which outputs a single winner) satisfies Condorcet Criterion and Participation simultaneously when the number of alternatives m is at least four. In this paper, we prove an extension of this impossibility theorem using smoothed analysis: for any fixed $m\ge 4$ and any voting rule r, under mild conditions, the smoothed likelihood for both Condorcet Criterion and Participation to be satisfied is at most $1-\Omega(n^{-3})$, where n is the number of voters that is sufficiently large. Our theorem immediately implies a quantitative version of the theorem for i.i.d. uniform distributions, known as the Impartial Culture in social choice theory.
    Date: 2021–07
  19. By: Andrea Attar (TSE - Toulouse School of Economics - UT1 - Université Toulouse 1 Capitole - Université Fédérale Toulouse Midi-Pyrénées - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CNRS - Centre National de la Recherche Scientifique); Eloisa Campioni (Unknown); Thomas Mariotti (TSE - Toulouse School of Economics - UT1 - Université Toulouse 1 Capitole - Université Fédérale Toulouse Midi-Pyrénées - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CNRS - Centre National de la Recherche Scientifique); Alessandro Pavan (Unknown)
    Abstract: We study games in which several principals contract with several privately-informed agents. We show that enabling the principals to engage in contractible private disclosures – by sending private signals to the agents about how the mechanisms will respond to the agents' messages – can significantly affect the predictions of such games. Our first result shows that private disclosures may generate equilibrium outcomes that cannot be supported in any game without private disclosures, no matter the richness of the message spaces and the availability of public randomizing devices. The result thus challenges the canonicity of the universal mechanisms of Epstein and Peters (1999). Our second result shows that equilibrium outcomes of games without private disclosures need not be sustainable when private disclosures are allowed. The result thus challenges the robustness of the "folk theorems" of Yamashita (2010) and Peters and Troncoso-Valverde (2013). These findings call for a novel approach to the analysis of competing-mechanism games.
    Keywords: Incomplete Information,Competing Mechanisms,Private Disclosures,Signals,Universal Mechanisms,Folk Theorems.
    Date: 2021–06–22
  20. By: Kunal Pattanayak; Vikram Krishnamurthy
    Abstract: This paper establishes the equivalence between Bayesian revealed preference and classical revealed preference with non-linear budget constraints. Classical revealed preference tests for utility maximization given known budget constraints. Bayesian revealed preference tests for costly information acquisition given a utility function. Our main result shows that the key theorem in Caplin and Dean (2015) on Bayesian revealed preference is equivalent to Afriat-type feasibility inequalities for general (non-linear) budget sets. Our second result exploits this equivalence of classical and Bayesian revealed preference to construct a monotone convex information acquisition cost from decision maker's data in Bayesian revealed preference
    Date: 2021–06

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