Optimal Auctions for Correlated Buyers with Sampling

Cr\'emer and McLean [1985] showed that, when buyers' valuations are drawn from a correlated distribution, an auction with full knowledge on the distribution can extract the full social surplus. We study whether this phenomenon persists when the auctioneer has only incomplete knowledge of the distribution, represented by a finite family of candidate distributions, and has sample access to the real distribution. We show that the naive approach which uses samples to distinguish candidate distributions may fail, whereas an extended version of the Cr\'emer-McLean auction simultaneously extracts full social surplus under each candidate distribution. With an algebraic argument, we give a tight bound on the number of samples needed by this auction, which is the difference between the number of candidate distributions and the dimension of the linear space they span

Interdependent Public Projects

In the interdependent values (IDV) model introduced by Milgrom and Weber [1982], agents have private signals that capture their information about different social alternatives, and the valuation of every agent is a function of all agent signals. While interdependence has been mainly studied for auctions, it is extremely relevant for a large variety of social choice settings, including the canonical setting of public projects. The IDV model is very challenging relative to standard independent private values, and welfare guarantees have been achieved through two alternative conditions known as {\em single-crossing} and {\em submodularity over signals (SOS)}. In either case, the existing theory falls short of solving the public projects setting. Our contribution is twofold: (i) We give a workable characterization of truthfulness for IDV public projects for the largest class of valuations for which such a characterization exists, and term this class \emph{decomposable valuations}; (ii) We provide possibility and impossibility results for welfare approximation in public projects with SOS valuations. Our main impossibility result is that, in contrast to auctions, no universally truthful mechanism performs better for public projects with SOS valuations than choosing a project at random. Our main positive result applies to {\em excludable} public projects with SOS, for which we establish a constant factor approximation similar to auctions. Our results suggest that exclusion may be a key tool for achieving welfare guarantees in the IDV model

A network solution to robust implementation:The case of identical but unknown distributions

Data de publicació electrònica: 24 de gener de 2023We study robust mechanism design in environments in which agents commonly believe that others’ types are identically distributed, but we do not assume that the actual distribution is common knowledge, nor that it is known to the designer. First, we characterize all incentive compatible transfers under these assumptions. Second, we characterize the conditions under which full implementation is possible via direct mechanisms, that only elicit payoff relevant information, and the transfer schemes which achieve it whenever possible. The full implementation results obtain from showing that the problem can be transformed into one of designing a network of strategic externalities, subject to suitable constraints which are dictated by the incentive compatibility requirements.The BSE benefited from the financial support of the Spanish Ministry of Economy and Competitiveness, through the Severo Ochoa Programme for Centres of Excellence in R&D (CEX2019-000915-S). Antonio Penta acknowledges the financial support of the European Research Council, Starting Grant 759424

Studies in Pricing Under Asymmetric Information

This dissertation consists of an introduction and three independent studies in pricing under asymmetric information. The introduction gives a broad motivation and a brief literature review for this dissertation. In the first study, we consider an economy where many sellers sell identical goods to many buyers. Each seller has a unit supply and each buyer has a unit demand. The only possible information flow about prices is through costly advertising. We show that in equilibrium the sellers use mixed strategies in pricing which leads to price and advertisement distributions. With convex advertising costs, each seller sends only one advertisement in the market. We also delineate a class of advertising costs which ensures that sellers may send multiple advertisements in equilibrium. Higher prices are advertised more than lower prices. In the second study, we consider a principal-agent model in which the principal can monitor and punish the agent with a fine if the agent is caught being untruthful. To reduce the probability of being verified, the agent can engage in costly avoidance. We design the optimal regulatory policies with and without avoidance. The optimal mechanism with enforcement allocates the object more often than the optimal mechanism without enforcement. Moreover, enforcement increases the expected transfers to the principal. Avoidance has two implications to the optimal regulatory mechanism: (i) the expected optimal transfers to the principal decrease and (ii) the principal allocates the object to a smaller share of types. If the latter effect dominates the former, it is possible that the agent's capability to engage in avoidance is disadvantageous not only for the principal, but also for the agent ex ante. In the third study, we derive the seller's utility maximizing selling mechanism in bilateral trade with interdependent values. Due to the interdependencies in valuations, finding the optimal mechanism is an informed seller problem. It turns out that the optimal mechanism is no longer a take-it-or-leave-it offer for the whole capacity; the seller finds it optimal to decrease the quantity of allocation (or the probability of trade) in order to credibly signal her private information to the buyer.Tämä väitöskirja koostuu johdannosta ja kolmesta itsenäisestä tutkimuksesta, jotka käsittelevät hinnoittelua epäsymmetrisen informaation vallitessa. Johdanto antaa laajan motivaation ja lyhyen kirjallisuuskatsauksen tälle väitöskirjalle. Ensimmäisessä tutkimuksessa tarkastelemme taloutta, jossa useat myyjät myyvät identtisiä hyödykkeitä usealle ostajalle. Jokaisella myyjällä on yksikkötarjonta ja jokaisella ostajalla yksikkökysyntä. Ainoa mahdollinen tiedonkulku hinnoista on mainonta. Osoitamme, että tasapainossa myyjät käyttävät hinnoittelussaan seka​​strategiaa, mikä johtaa siihen, että markkinoilla kysytään useaa eri hintaa ja lähetetään eri määriä mainoksia. Jos mainostuskulut ovat konveksit, jokainen myyjä lähettää vain yhden mainoksen markkinoille. Jos puolestaan mainostuskustannukset kuuluvat tiettyyn konkaavien kustannusten luokkaan, myyjät lähettävät useita mainoksia tasapainossa. Korkeampia hintoja mainostetaan enemmän kuin alhaisempia hintoja, mikä tukee empiirisen kirjallisuuden evidenssiä. Toisessa tutkimuksessa tarkastelemme päämies–agentti-mallia, jossa päämiehellä on käytössään lain täytäntöönpanovalta, jolla hän voi monitoroida agentin käyttäytymistä ja rankaista häntä sakolla, jos agentti ei käyttäydy lainmukaisesti. Kiinnijäämistodennäköisyyden vähentämiseksi agentti voi investoida kiinnijäämisen välttelyyn. Suunnittelemme erikseen optimaaliset regulaatiomekanismit kun agentti voi, ja ei voi, investoida kiinnijäämisen välttelyyn. Optimaalinen mekanismi lain täytäntöönpanovallla allokoi objektin (esimerkiksi toimiluvan tai hyödykkeen) useammin kuin optimaalinen mekanismi ilman verifikaatiota. Lisäksi täytäntöönpano lisää odotettavissa olevia tuottoja päämiehelle. Agentin mahdollisuudella vältellä kiinnijäämistä on kaksi vaikutusta optimaaliseen säätelymekanismiin: (i) odotetut tulonsiirrot päämiehelle pienenevät ja (ii) päämies allokoi objektin pienemmälle osalle agentin tyyppejä. Jos jälkimmäinen vaikutus on suurempi kuin ensimmäinen, on mahdollista, että agentin kyky vältellä kiinnijäämistä on epäedullinen molemmille, agentille ja päämiehelle. Kolmannessa tutkimuksessa tutkimme "sitruunoiden" markkinoita (the market for lemons) mekanisminsuunnittelun näkökulmasta kahdenvälisessä kaupan järjestelyssä. Ratkaisemme suljetun muodon ratkaisun myyjän optimaaliselle ja riskittömälle (safe) myyntimekanismille kun ainoastaan myyjällä on yksityistä tietoa tuotteen laadusta. Osoitamme, että myyjät voivat paljastaa tavaroidensa laadun kontrolloimalla tavaroidensa tarjontaa; laadukkaita tuotteita tarjoavat myyjät haluavat tavaroidensa olevan niukkoja ja kalliita, kun taas huonolaatuisten tuotteiden myyjät haluavat tuotteitaan olevan runsaasti tarjolla halpaan hintaan. Tällä tavalla myyjät voivat erottaa tuotteensa toisistaan ​​ja maksimoida voittojaan. Laajennamme tätä mallin siten, että myös myyjällä on yksityistä tietoa tuotteen arvosta. Johdamme uudenlaisen karakterisaation myyjän kannalta optimaalisesta ja riskittömästä myyntimekanismista. Osoittautuu, että jos kahdenvälisessä kaupassa on molemminpuolista epäsymmetristä informaatiota, niin myyjä myy koko kapasiteetin ja siten harjoittaa ainoastaan hintasignalointia määräsignaloinnin sijaan. Toisin sanoen, hintasignalointi on myyjälle edullisin tapa paljastaa tuotteen laatu ostajalle tässä tapauksessa

Full Implementation and Belief Restrictions

Multiplicity of equilibria and the dependence on strong common knowledge assumptions are well-known problems in mechanism design. We address them by studying full implementation via transfer schemes, under general restrictions on agents' beliefs. We show that incentive-compatible transfers ensure uniqueness-and hence full implementation-if they induce sufficiently weak strategic externalities. We then design transfers for full implementation by using information on beliefs in order to weaken the strategic externalities of the baseline canonical transfers. Our results rely on minimal restrictions on agents' beliefs, specifically on moments of the distribution of types, that arise naturally in applications. (JEL D62, D82, D83

Essays on Auction Design

This dissertation studies the design of auction markets where bidders are uncertain of their own values at the time of bidding. A bidder's value may depend on other bidders' private information, on total quantity of items allocated in the auction, or on the auctioneer's private information. Chapter 1 provides a brief introduction to auction theory and summarizes the main contribution of each following chapter. Chapter 2 of this dissertation extends the theoretical study of position auctions to an interdependent values model in which each bidder's value depends on its opponents' information as well as its own information. I characterize the equilibria of three standard position auctions under this information structure, including the Generalized Second Price (GSP) auctions, Vickrey-Clarke-Groves (VCG) auctions, and the Generalized English Auctions (GEA). I first show that both GSP and VCG auctions are neither efficient nor optimal under interdependent values. Then I propose a modification of these two auctions by allowing bidders to condition their bids on positions to implement efficiency. I show that the modified auctions proposed in this chapter are not only efficient, but also maximize the search engine's revenue. While the uncertainty of each bidder about its own value comes from the presence of common component in bidders’ ex-post values in an interdependent values model, bidders can be uncertain about their values when their values depend on the entire allocation of the auction and when their values depend on the auctioneer's private information. Chapter 3 of this dissertation studies the design of efficient auctions and optimal auctions in a license auction market where bidders care about the total quantity of items allocated in the auction. I show that the standard uniform-price auction and the ascending clock auction are inefficient when the total supply needs to be endogenously determined within the auction. Then I construct a multi-dimensional uniform-price auction and a Walrasian clock auction that can implement efficiency in a dominant strategy equilibrium under surplus-maximizing reserve prices and achieve optimal revenue under revenue-maximizing reserve prices. Chapter 4 of this dissertation analyzes an auctioneer's optimal information provision strategy in a procurement auction in which the auctioneer has private preference over bidders' non-price characteristics and bidders invest in cost-reducing investments before entering the auction. I show that providing more information about the auctioneer's valuation over bidders' non-price characteristics encourages those favored bidders to invest more and expand the distribution of values in the auction. Concealment is the optimal information provision policy when there are two suppliers