
on Microeconomics 
By:  Smolin, Alex; Ichihashi, Shota 
Abstract:  A seller faces a consumer with an uncertain value for the product. The seller has imperfect private information about the value and requests additional data to set the price. The consumer can decline any request. The consumer’s willingness to provide data depends on his belief about the seller’s type which in turn depends on the request. We show that the type uncertainty limits the scope of data collection: All equilibrium payoffs are spanned by fully pooling equilibria in which the seller collects the same data regardless of the type. The seller’s private information lowers efficiency and profits, but benefits the consumer by fueling his skepticism and preventing excessive data collection. Having less private information may enable the seller to collect more data directly from the consumer and may lower the overall consumer welfare. 
Keywords:  consumer privacy; data collection; information design; mechanism design; price discrimination 
JEL:  D42 D82 D83 
Date:  2022–04–19 
URL:  http://d.repec.org/n?u=RePEc:tse:wpaper:126871&r= 
By:  Majid Mahzoon 
Abstract:  We study strategic information transmission in a hierarchical setting where information gets transmitted through a chain of agents up to a decision maker whose action is of importance to every agent. This situation could arise whenever an agent can communicate to the decision maker only through a chain of intermediaries, for example, an entrylevel worker and the CEO in a firm, or an official in the bottom of the chain of command and the president in a government. Each agent can decide to conceal part or all the information she receives. Proving we can focus on simple equilibria, where the only player who conceals information is the first one, we provide a tractable recursive characterization of the equilibrium outcome, and show that it could be inefficient. Interestingly, in the binaryaction case, regardless of the number of intermediaries, there are a few pivotal ones who determine the amount of information communicated to the decision maker. In this case, our results underscore the importance of choosing a pivotal vice president for maximizing the payoff of the CEO or president. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.05304&r= 
By:  Martin Peitz; Lily Samkharadze 
Abstract:  Platform competition can be intense when offering nondifferentiated services. However, competition is somewhat relaxed if platforms cannot set negative prices. If platforms collude they may be able to implement the outcome that maximizes industry profits. In an infinitely repeated game with perfect monitoring, this is feasible if the discount factor is sufficiently large. When this is not possible, under some condition, a collusive outcome with onesided rent extraction along the equilibrium path can be sustained that leads to higher profits than the noncooperative outcome. 
Keywords:  Twosided markets, tacit collusion, cartelization, price structure, platform competition 
JEL:  L41 L13 D43 
Date:  2022–01 
URL:  http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2022_331v1&r= 
By:  Sahm, Marco 
Abstract:  I characterize the optimal accuracy level r of an unbiased Tullock contest between two players with heterogeneous prize valuations. The designer maximizes the winning probability of the strong player or the winner's expected valuation by choosing a contest with an allpay auction equilibrium (r ≥ 2). By contrast, if she aims at maximizing the expected aggregate effort or the winner's expected effort, she will choose a contest with a purestrategy equilibrium, and the optimal accuracy level r 
Keywords:  Tullock Contest,Heterogeneous Valuations,Accuracy,Discrimination,Optimal Design,AllPay Auction 
JEL:  C72 D72 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:zbw:bamber:175&r= 
By:  Hammond, Peter J. (Dept. of Economics, University of Warwick) 
Abstract:  Following previous work on consequentialist decision theory, we consider an unrestricted domain of finite decision trees, including continuation subtrees, with : (i) decision nodes where the decision maker must make a move ; (ii) chance nodes at which a â€œroulette lotteryâ€ with exogenously specified strictly positive probabilities is resolved ; (iii) event nodes at which a â€œhorse lotteryâ€ is resolved. A complete family of binary conditional base preference relations over Anscombeâ€“Aumann lottery consequences is defined to be â€œprerationalâ€ just in case there exists a behaviour rule that is defined throughout the tree domain which is explicable as avoiding, under all predictable circumstances, consequences that are regrettable given what is feasible. Prerationality is shown to hold if and only if all conditional base preference relations are complete and transitive, while also satisfying both the independence axiom of expected utility theory and a strict form of Anscombe and Aumannâ€™s extension of Savageâ€™s sure thing principle. Assuming that the base relations satisfy nontriviality and a generalized form of state independence that holds even when consequence domains are state dependent, prerationality combined with continuity on Marschak triangles is equivalent to representation by a refined subjective expected utility function that excludes zero probabilities. 
Keywords:  Prerational base relations ; rational planning ; decision trees ; regrettable consequences ; Anscombeâ€“Aumann lotteries ; preference ordering ; independence axiom ; surething principle ; subjective probability ; subjective expected utility ; Bayesian rationality ; state independence JEL codes: D81 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:wrk:wcreta:72&r= 
By:  Hiroki Shinozaki; Tomoya Kazumura; Shigehiro Serizawa 
Abstract:  We consider the problem of allocating multiple units of an object and collecting payments. Each agent can receive multiple units, and his (consumption) bundle is a pair consisting of the units he receives and his payment. An agent’s preference over bundles may not be quasilinear. A class of preferences is rich if it includes all quasilinear preferences with constant incremental valuations. We show that for an odd number of units, if a class of preferences is rich and includes at least one preference exhibiting both decreasing incremental valuations and either positive or negative income effects, then no rule satisfies efficiency, individual rationality, no subsidy for losers, and strategyproofness. In contrast, for an even number of units, the existence of a rule satisfying the four properties depends on the size of the income effects. We further show that if a rich class of preferences includes only preferences that exhibit nondecreasing incremental valuations, then the generalized Vickrey rule (Saitoh and Serizawa, 2008; Sakai, 2008) is the only rule satisfying the four properties. Our results suggest that (i) there a rule satisfying the four properties “almost” only when preferences exhibit nondecreasing incremental valuations, and (ii) it depends not only on the properties of preferences such as nondecreasing incremental valuations, but also on other characteristics of the environment such as the number of units. 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:dpr:wpaper:1097r&r= 
By:  Takashi Ui 
Abstract:  Interacting agents receive public information at no cost and flexibly acquire private information at a cost proportional to entropy reduction. When a policymaker provides more public information, agents acquire less private information, thus lowering information costs. Does more public information raise or reduce uncertainty faced by agents? Is it beneficial or detrimental to welfare? To address these questions, we examine the impacts of public information on flexible information acquisition in a linearquadraticGaussian game with arbitrary quadratic material welfare. More public information raises uncertainty if and only if the game exhibits strategic complementarity, which can be harmful to welfare. However, when agents acquire a large amount of information, more provision of public information increases welfare through a substantial reduction in the cost of information. We give a necessary and sufficient condition for welfare to increase with public information and identify optimal public information disclosure, which is either full or partial disclosure depending upon the welfare function and the slope of the best response. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.09250&r= 
By:  Dütting, Paul; Kesselheim, Thomas 
Abstract:  In a combinatorial auction with item bidding, agents participate in multiple singleitem secondprice auctions at once. As some items might be substitutes, agents need to strategize in order to maximize their utilities. A number of results indicate that high social welfare can be achieved this way, giving bounds on the welfare at equilibrium. Recently, however, criticism has been raised that equilibria of this game are hard to compute and therefore unlikely to be attained. In this paper, we take a different perspective by studying simple bestresponse dynamics. Often these dynamics may take exponentially long before they converge or they may not converge at all. However, as we show, convergence is not even necessary for good welfare guarantees. Given that agents’ bid updates are aggressive enough but not too aggressive, the game will reach and remain in states of high welfare after each agent has updated his bid at least once. 
Keywords:  algorithmic game theory; combinatorial auctions; item bidding; bestresponse dynamics 
JEL:  J1 
Date:  2020–10–01 
URL:  http://d.repec.org/n?u=RePEc:ehl:lserod:106607&r= 
By:  Zhaohua Chen; Xiaotie Deng; Jicheng Li; Chang Wang; Mingwei Yang 
Abstract:  In today's online advertising markets, it is common for an advertiser to set a longperiod budget. Correspondingly, advertising platforms adopt budget control methods to ensure that any advertiser's payment is within her budget. Most budget control methods rely on value distributions of advertisers. However, due to the complex environment advertisers stand in and privacy issues, the platform hardly learns their true priors. Therefore, it is essential to understand how budget control auction mechanisms perform under unassured priors. This paper gives a twofold answer. First, we propose a biddiscount method barely studied in the literature. We show that such a method exhibits desirable properties in revenuemaximizing and computation when fitting into firstprice auction. Second, we compare this mechanism with another four in the prior manipulation model, where an advertiser can arbitrarily report a value distribution to the platform. These four mechanisms include the optimal mechanism satisfying budgetconstrained IC, firstprice/secondprice mechanisms with the widelystudied pacing method, and an application of biddiscount in secondprice mechanism. We consider three settings under the model, depending on whether the reported priors are fixed and advertisers are symmetric or not. We show that under all three cases, the biddiscount firstprice auction we introduce dominates the other four mechanisms concerning the platform's revenue. For the advertisers' side, we show a surprising strategicequivalence result between this mechanism and the optimal auction. Extensive revenue dominance and strategic relationships among these mechanisms are also revealed. Based on these findings, we provide a thorough understanding of prior dependency in repeated auctions with budgets. The biddiscount firstprice auction itself may also be of further independent research interest. 
Date:  2022–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2203.16816&r= 
By:  Angelika EndresFröhlich (Paderborn University); Joachim Heinzel (Paderborn University) 
Abstract:  Research has found that downstream bundling aggravates the problem of double marginalization in a decentralized channel, but reduces the intensity of downstream price competition when trading homogeneous goods. We study the validity of those results in a setup where the traded goods have heterogeneous product qualities. We find that the quality relation between the goods determines whether the competition reduction effect of bundling outweighs the aggravation of double marginalization in a decentralized channel. Thus, the quality relation between the goods determines the profitability of downstream bundling. The underlying market consists of a distribution channel with two downstream firms and two pricesetting monopolistic upstream producers. One upstream firm sells good 1 exclusively to one downstream firm and the other upstream firm sells good 2 to both downstream firms. The downstream firms compete in prices and the twoproduct downstream firm has the option to bundle both goods. In particular, we find bundling to be profitable for the twoproduct downstream firm only when the quality of good 2 exceeds the quality of good 1. However, we find bundling always to be profitable when the production process is controlled by the downstream industry. The impact on total welfare is ambiguous and depends on the distribution of market power in the channel and the quality levels of the goods. 
Keywords:  double marginalization; downstream bundling; leverage theory; quality differentiation 
JEL:  D21 D61 L11 L15 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:pdn:dispap:90&r= 
By:  Chinmay Maheshwari; Kshitij Kulkarni; Manxi Wu; Shankar Sastry 
Abstract:  How can a social planner adaptively incentivize selfish agents who are learning in a strategic environment to induce a socially optimal outcome in the long run? We propose a twotimescale learning dynamics to answer this question in both atomic and nonatomic games. In our learning dynamics, players adopt a class of learning rules to update their strategies at a faster timescale, while a social planner updates the incentive mechanism at a slower timescale. In particular, the update of the incentive mechanism is based on each player's externality, which is evaluated as the difference between the player's marginal cost and the society's marginal cost in each time step. We show that any fixed point of our learning dynamics corresponds to the optimal incentive mechanism such that the corresponding Nash equilibrium also achieves social optimality. We also provide sufficient conditions for the learning dynamics to converge to a fixed point so that the adaptive incentive mechanism eventually induces a socially optimal outcome. Finally, we demonstrate that the sufficient conditions for convergence are satisfied in a variety of games, including (i) atomic networked quadratic aggregative games, (ii) atomic Cournot competition, and (iii) nonatomic network routing games. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.05507&r= 
By:  Yann Bramoullé (AMSE  AixMarseille Sciences Economiques  EHESS  École des hautes études en sciences sociales  AMU  Aix Marseille Université  ECM  École Centrale de Marseille  CNRS  Centre National de la Recherche Scientifique); Brian Rogers (WUSTL  Washington University in Saint Louis); Erdem Yenerdag (WUSTL  Washington University in Saint Louis) 
Abstract:  We study a twoperiod onetoone dynamic matching environment in which agents meet randomly and decide whether to match early or defer. Crucially, agents can match with either partner in the second period. This "recall" captures situations where, e.g., a firm and worker can conduct additional interviews before contracting. Recall has a profound impact on incentives and on aggregate outcomes. We show that the likelihood to match early is nonmonotonic in type: early matches occur between the goodbutnotbest agents. The option value provided by the firstperiod partner provides a force against unraveling, so that deferrals occur under small participation costs. 
Keywords:  recall,unraveling,dynamic matching 
Date:  2022–02–14 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:halshs03602169&r= 
By:  JinWook Chang; Matt Darst 
Abstract:  This paper studies competitive market shutdowns due to adverse selection, where sellers post nonexclusive menus of contracts. We first show that the presence of the worst type of agents (moldy lemons) causes markets to fail only if their mass is sufficiently large. We then show that a small mass of moldy lemons can lead to a large cascade of exits when buyers possess outside options. Our results suggest a parsimonious way of generating sudden market shutdowns without relying on institutional details or imposing additional structure on the model. Thus, the simple insights on the properties of market shutdowns we consider are applicable to many different markets and contexts. 
Keywords:  Asymmetric information; Market unraveling; Nonexclusive contracting 
JEL:  D52 D53 D82 E44 G32 
Date:  2022–03–23 
URL:  http://d.repec.org/n?u=RePEc:fip:fedgfe:202213&r= 
By:  Felix Brandt; Chris Dong 
Abstract:  We introduce a new notion of rationalizability where the rationalizing relation may depend on the set of feasible alternatives. More precisely, we say that a choice function is locally rationalizable if it is rationalized by a family of rationalizing relations such that a strict preference between two alternatives in some feasible set is preserved when removing other alternatives. We then show that a choice function is locally rationalizable if and only if it satisfies Sen's $\gamma$ and give similar characterizations for local rationalizability via transitive, PIPtransitive, and quasitransitive relations. Local rationalizability is realized via families of revealed preference relations that are sandwiched in between the base relation and the revealed preference relation of a choice function. We demonstrate the adequacy of our results for analyzing and constructing consistent social choice functions by giving simple characterizations of the top cycle and the uncovered set using transitive and quasitransitive local rationalizability. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.05062&r= 
By:  Gani Aldashev (ECARES, SBSEM, Université libre de Bruxelles); Esteban Jaimovich (University of Surrey); Thierry Verdier (PSE/École des PontsParisTech/PUC Rio/CEPR) 
Abstract:  We study the implications of transparency policies on decentralized public good provision. The moral hazard inside nonprofits interacts with the competitive structure of the sector under alternative informational regimes. More transparency on the use of funds has an ambiguous e§ect on the total public good provision and donors’ welfare. Transparency encourages nonprofits to more actively curb rentseeking inside organizations, but it also tilts the playing field against nonprofits facing higher monitoring costs, inducing them to abandon their missions and reducing nonprofit diversity. Donors’ welfare is lower under transparency for intermediate levels of asymmetry in monitoring costs. 
Keywords:  public goods, nonprofit organizations, charitable giving, altruism, transparency. 
JEL:  L31 D64 D43 D23 
Date:  2022–03 
URL:  http://d.repec.org/n?u=RePEc:aoz:wpaper:125&r= 
By:  Bhavook Bhardwaj; Siddharth Chatterjee 
Abstract:  The standard economic model of choice assumes that a decision maker chooses from sets of alternatives. A new branch of literature has considered the problem of choosing from lists i.e. ordered sets. In this paper, we propose a new framework that considers choice from infinite sequences. Our framework provides a natural way to model decision making in settings where choice relies on a string of recommendations. We introduce three broad classes of choice rules in this framework. Our main result shows that bounded attention is due to the continuity of the choice functions with respect to a natural topology. We introduce some natural choice rules in this framework and provide their axiomatic characterizations. Finally, we introduce the notion of computability of a choice function using Turing machines and show that computable choice rules can be implemented by a finite automaton. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2203.00070&r= 
By:  Yusuke Kamishiro; Rajiv Vohra; Roberto Serrano 
Abstract:  This paper provides a noncooperative approach to core stability in an economy with incomplete information. The analysis covers general exchange economies, although our tightest results hold when effective coalitions consist of at most two players, as in matching. We study the perfect Bayesian equilibria of an extensive form mechanism that extends the one used by Serrano and Vohra (1997) to implement the core of a complete information economy. This leads to a version of the core that we refer to as the sequential core, which allows for information to be transmitted among the agents during the process of coalition formation. Such information flows include proposals that can be viewed as signaling devices and/or screening contracts. The same result is obtained in a model of infinitehorizon coalitional bargaining for stationary PBE. Equilibrium refinements are then used to provide justifications for the coarse core and the fine core. 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:bro:econwp:2022001&r= 
By:  Christa Cuchiero; Guido Gazzani; Irene Klein 
Abstract:  We introduce two kinds of risk measures with respect to some reference probability measure, which both allow for a certain order structure and domination property. Analyzing their relation to each other leads to the question when a certain minimax inequality is actually an equality. We then provide conditions under which the corresponding robust risk measures, being defined as the supremum over all risk measures induced by a set of probability measures, can be represented classically in terms of one single probability measure. We focus in particular on the mixture probability measure obtained via mixing over a set of probability measures using some prior, which represents for instance the regulator's beliefs. The classical representation in terms of the mixture probability measure can then be interpreted as a Bayesian approach to robust risk measures. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.07115&r= 
By:  Nick Netzer; Arthur Robson; Jakub Steiner; Pavel Kocourek 
Abstract:  In a model inspired by neuroscience, we show that constrained optimal perception encodes lottery rewards using an Sshaped encoding function and oversamples lowprobability events. The implications of this perception strategy for behavior depend on the decisionmaker’s understanding of the risk. The strategy does not distort choice in the limit as perception frictions vanish when the decisionmaker fully understands the decision problem. If, however, the decisionmaker underrates the complexity of the decision problem, then risk attitudes reflect properties of the perception strategy even for vanishing perception frictions. The model explains adaptive risk attitudes and probability weighting as in prospect theory and, additionally, predicts that risk attitudes are strengthened by time pressure and attenuated by anticipation of large risks. 
Keywords:  endogenous preferences, probability distortions, misspecified learning 
JEL:  D81 D87 D91 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:ces:ceswps:_9547&r= 
By:  Axel Gautier (LCII  Liège Competition and Innovation Institute, HEC Liège); JeanChristophe Poudou; Michel Roland (CREATE  ULaval  Université Laval [Québec], ULaval  Université Laval [Québec]) 
Abstract:  This paper analyzes whether repealing net neutrality (NN) improves or decreases the capacity of a regulator to make internet service providers (ISPs) extend broadband coverage through universal service obligations (USOs). We model a twosided market where a monopolistic ISP links content providers (CPs) to end users with a broadband network of a given bandwidth. A regulator determines whether to submit the ISP to NN or to allow it to supply paid priority (P) services to CPs. She can also impose a broadband USO to the ISP, i.e. she can mandate the broadband market coverage. We show that the greater is the network bandwidth, the more likely the repeal of net neutrality increases ISP profits and social welfare. Regulation can still be necessary, however, as there are bandwidth ranges for which the ISP would benefit from a repeal of NN while such a repeal is detrimental to society. 
Keywords:  L96,Internet,Net Neutrality,Universal Service Obligations,Prioritization,Regulation JEL: D21,K23,L12,L51 
Date:  2022–03–07 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal03609917&r= 