
on Microeconomics 
By:  Patrick Rey (TSE  Toulouse School of Economics  UT1  Université Toulouse 1 Capitole  Université Fédérale Toulouse MidiPyrénées  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 MidiPyrénées  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 nonrepeated 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,Informationlight regulation,Price caps 
Date:  2019–12 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal03270038&r= 
By:  Antoine Dubus (Télécom ParisTech) 
Abstract:  This article analyzes behaviorbased price discrimination in a twoperiod competition framework where firms endogenously collect consumer data and strategically target past customers. When firms strategically target customers: (i) they pricediscriminate 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:  Behaviorbased price discrimination,Strategic Targeting,Data collection 
Date:  2021–06–24 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal03269586&r= 
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 productbyproduct revenue curves are singlepeaked. 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 singleitem prices: upgrade pricing and separate pricing are equivalent. 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.10323&r= 
By:  Francisco Rodr\'iguez; Eduardo Zambrano 
Abstract:  In this paper, we show that when policymotivated parties can commit to a particular platform during a unidimensional 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 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.07910&r= 
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 pointthe search scopeis 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 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:29008&r= 
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 marketmaker 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 
URL:  http://d.repec.org/n?u=RePEc:iza:izadps:dp14524&r= 
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 secondorder distribution. Realistically, investors may also have multiple priors about the secondorder 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, thirdorder probabilities 
JEL:  D81 G11 
Date:  2020–06 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:108837&r= 
By:  Marcelo Ariel Fernandez; Kirill Rudov; Leeat Yariv 
Abstract:  We study the impacts of incomplete information on centralized onetoone matching markets. We focus on the commonly used Deferred Acceptance mechanism (Gale and Shapley, 1962). We show that many completeinformation results are fragile to a small infusion of uncertainty about others' preferences. 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.04098&r= 
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 mixedVCG 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. MixedVCG uses data distortions as data money for this purpose. We further relax zero cost data distortion assumption by proposing distortedmixedVCG. We also extend our model and results to data sharing via incremental inquiries and differential privacy costs. 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.08630&r= 
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 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2106.16047&r= 
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 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.06312&r= 
By:  Gabriel P. Andrade; Rafael Frongillo; Elliot Gorokhovsky; Sharadha Srinivasan 
Abstract:  Kakade, Kearns, and Ortiz (KKO) introduce a graphtheoretic generalization of the classic ArrowDebreu (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 longrange 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 auctionbased algorithm to compute approximate equilibria when agent utilities satisfy the weak grosssubstitutes property. 
Date:  2021–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2106.14397&r= 
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 Mallowsdistributed preferences for four common assignment mechanisms. 
Date:  2021–07–22 
URL:  http://d.repec.org/n?u=RePEc:osf:socarx:xt37c&r= 
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 $\gamma\in (1, \frac{c}{c1}]$, 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 closedform 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 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.01947&r= 
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 PanthéonSorbonne  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 PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique); NgocSang 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.,Nonconvex preferences 
Date:  2021–03–23 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:halshs03177843&r= 
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 firstorder 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 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2106.16081&r= 
By:  Philippe Jehiel; Konrad Mierendorff 
Abstract:  We consider auction environments in which at the time of the auction bidders observe signals about their expost 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 steadystates in such environments, and importantly we allow for correlation in the signal distribution. We first observe that datadriven bidders may behave suboptimally in classical auctions such as the secondprice or firstprice auctions whenever there are correlations. Allowing for a mix of rational (or experienced) and datadriven (novice) bidders results in inefficiencies in such auctions, and we show the inefficiency extends to all auctionlike mechanisms in which bidders are restricted to submit onedimensional (realvalued) bids. 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.00640&r= 
By:  Lirong Xia 
Abstract:  In 1988, Moulin proved an insightful and surprising impossibility theorem that reveals a fundamental incompatibility between two commonlystudied 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 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.06435&r= 
By:  Andrea Attar (TSE  Toulouse School of Economics  UT1  Université Toulouse 1 Capitole  Université Fédérale Toulouse MidiPyrénées  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 MidiPyrénées  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 privatelyinformed 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 TroncosoValverde (2013). These findings call for a novel approach to the analysis of competingmechanism games. 
Keywords:  Incomplete Information,Competing Mechanisms,Private Disclosures,Signals,Universal Mechanisms,Folk Theorems. 
Date:  2021–06–22 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal03266804&r= 
By:  Kunal Pattanayak; Vikram Krishnamurthy 
Abstract:  This paper establishes the equivalence between Bayesian revealed preference and classical revealed preference with nonlinear 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 Afriattype feasibility inequalities for general (nonlinear) 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 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2106.14486&r= 