Papers by Isa Emin Hafalir
Sort-cut: A pareto optimal and semi-truthful mechanism for multi-unit auctions with budget-constrained bidders. Ad Auctions Workshop
Motivated by sponsored search auctions with hard budget constraints given by the adver-tisers, we... more Motivated by sponsored search auctions with hard budget constraints given by the adver-tisers, we study multi-unit auctions of a single item. An important example is a sponsored result slot for a keyword, with many units representing its inventory in a month, say. In this single-item multi-unit auction, each bidder has a private value for each unit, and a private bud-get which is the total amount of money she can spend in the auction. A recent impossibility result [Dobzinski et al., FOCS’08] precludes the existence of a truthful mechanism with Pareto-optimal allocations in this important setting. We propose Sort-Cut, a mechanism which does the next best thing from the auctioneer’s point of view, that we term semi-truthful. While we are unable to give a complete characterization of equilibria for our mechanism, we prove that some equilibrium of the proposed mechanism optimizes the revenue over all Pareto-optimal mech-anisms, and that this equilibrium is the unique one resulting from ...
Motivated by sponsored search auctions with hard budget constraints given by the adver-tisers, we... more Motivated by sponsored search auctions with hard budget constraints given by the adver-tisers, we study multi-unit auctions of a single item. An important example is a sponsored result slot for a keyword, with many units representing its inventory in a month, say. In this single-item multi-unit auction, each bidder has a private value for each unit, and a private bud-get which is the total amount of money she can spend in the auction. A recent impossibility result [Dobzinski et al., FOCS’08] precludes the existence of a truthful mechanism with Pareto-optimal allocations in this important setting. We propose Sort-Cut, a mechanism which does the next best thing from the auctioneer’s point of view, that we term semi-truthful. While we are unable to give a complete characterization of equilibria for our mechanism, we prove that some equilibrium of the proposed mechanism optimizes the revenue over all Pareto-optimal mech-anisms, and that this equilibrium is the unique one resulting from ...
Rev. Econ. Design DOI 10.1007/s10058-011-0110-6 ORIGINAL PAPER Selling goods of unknown quality: forward versus spot auctions
We consider an environment where the sale can take place so early that both the seller and potent... more We consider an environment where the sale can take place so early that both the seller and potential buyers have the same uncertainty about the quality of the good. We present a simple model that allows the seller to offer the good for sale before or after this uncertainty is resolved, namely via forward auction or spot auction, respectively. We solve for the equilibrium of these two auctions and then compare the resulting expected revenues. We also consider the revenue implications of insurance in forward auctions.
Motivated by sponsored search auctions with hard budget constraints given by the advertisers, we ... more Motivated by sponsored search auctions with hard budget constraints given by the advertisers, we study multi-unit auctions of a single item. An important example is a sponsored result slot for a keyword, with many units representing its inventory in a month, say. In this single-item multi-unit auction, each bidder has a private value for each unit, and a private budget which is the total amount of money she can spend in the auction. A recent impossibility result [Dobzinski et al., FOCS’08] precludes the existence of a truthful mechanism with Pareto-optimal allocations in this important setting. We propose Sort-Cut, a mechanism which does the next best thing from the auctioneer’s point of view, that we term semitruthful. In our mechanism, it is a weakly dominant strategy for all agents to state their true budgets and to not understate their values.
College Admissionswith Entrance Exams
We study a college admissions problem in which colleges accept students by ranking students' ... more We study a college admissions problem in which colleges accept students by ranking students' efforts in entrance exams. Students' ability levels affect the cost of their efforts. We solve and compare the equilibria of "centralized college admissions" (CCA) where students apply to all colleges and "decentralized college admissions" (DCA) where students only apply to one college. We show that lower ability students prefer DCA whereas higher ability students prefer CCA. Many predictions of the theory are supported by a lab experiment designed to test the theory, yet we find a number of differences that render DCA less attractive than CCA compared to the equilibrium benchmark.
This thesis consists of three chapters. In the first chapter, we consider coalition formation gam... more This thesis consists of three chapters. In the first chapter, we consider coalition formation games with externalities. A natural extension of superadditivity is not sufficient to imply that the grand coalition is efficient when externalities are present. We provide a condition, analogous to convexity, that is sufficient for the grand coalition to be efficient and show that this also implies that the (appropriately defined) core is nonempty. Moreover, we propose a mechanism which implements the most efficient partition for all coalition formation games and characterize the resulting payoff division. The second chapter, written jointly with Vijay Krishna, studies equilibria of first-and second-price auctions with resale in a model with independent private values. With asymmetric bidders, the resulting inefficiencies create a motive for post-auction trade. In our basic model, resale takes place via monopoly pricingthe winner of the auction makes a take-it-or-leave-it offer to the loser after updating his prior beliefs based on his winning. We show that a first-price auction with resale has a unique monotonic equilibrium. Our main result is that with resale, the expected revenue from a first-price auction exceeds that from a second-price auction. The results extend to other resale mechanisms: monopsony and, more generally, probabilistic k-double auctions. The inclusion of resale possibilities thus permits a general revenue ranking of the two auctions that is not available when these are excluded. The third chapter, written jointly with Vijay Krishna, studies first-price auctions in a model with asymmetric, independent private values. Our goal is to compare equilibria of the first-price auction without resale (FPA) with those of the first-price auction with resale (FPAR). For the two major families of distributions for which equilibria of the FPA are available in closed form, we show that resale possibilities increase the revenue of the original seller. We also show by example that, somewhat paradoxically, resale may actually decrease efficiency.
ArXiv, 2009
Motivated by sponsored search auctions with hard budget constraints given by the advertisers, we ... more Motivated by sponsored search auctions with hard budget constraints given by the advertisers, we study multi-unit auctions of a single item. An important example is a sponsored result slot for a keyword, with many units representing its inventory in a month, say. In this single-item multi-unit auction, each bidder has a private value for each unit, and a private budget which is the total amount of money she can spend in the auction. A recent impossibility result [Dobzinski et al., FOCS’08] precludes the existence of a truthful mechanism with Paretooptimal allocations in this important setting. We propose Sort-Cut, a mechanism which does the next best thing from the auctioneer’s point of view, that we term semi-truthful. While we are unable to give a complete characterization of equilibria for our mechanism, we prove that some equilibrium of the proposed mechanism optimizes the revenue over all Pareto-optimal mechanisms, and that this equilibrium is the unique one resulting from a na...
Discriminatory auctions with resale
Economic Theory Bulletin
We consider multi-unit discriminatory auctions where ex ante symmetric bidders have single-unit d... more We consider multi-unit discriminatory auctions where ex ante symmetric bidders have single-unit demands and resale is allowed after the bidding stage. When bidders use the optimal auction to sell items in the resale stage, the equilibrium in the auction without resale is no longer an equilibrium in an auction with resale. We find a symmetric and monotone equilibrium when there are two units for sale, and, interestingly, we show that there may not be a symmetric and monotone equilibrium if there are more than two units.
Integrating School Districts: Diversity, Balance, and Welfare
SSRN Electronic Journal
Despite significant efforts, segregation in the US public schools still persists. It mainly occur... more Despite significant efforts, segregation in the US public schools still persists. It mainly occurs between, but not within, school districts. To overcome this problem, inter-district admissions have been introduced, and many school districts have been integrated in a handful of states. We study district integration from a market-design perspective. For each desired policy, we provide admission rules and algorithms so that the policy goal is established. We provide a novel framework that opens avenues for market-design research.
SSRN Electronic Journal
A. Interdistrict school choice programs-where a student can be assigned to a school outside of he... more A. Interdistrict school choice programs-where a student can be assigned to a school outside of her district-are widespread in the US, yet the market-design literature has not considered such programs. We introduce a model of interdistrict school choice and present two mechanisms that produce stable or efficient assignments. We consider three categories of policy goals on assignments and identify when the mechanisms can achieve them. By introducing a novel framework of interdistrict school choice, we provide a new avenue of research in market design.
Mathematical Social Sciences
Certain aggregate externalities, like those due to knowledge and public goods, do not change very... more Certain aggregate externalities, like those due to knowledge and public goods, do not change very much in response to changes in two individuals' actions. Thus, individuals rationally regard the level of the externality as fixed in their negotiations with each other. We leverage this observation to develop a general framework for the existence of stable matchings in moderately sized one-to-one matching games, and we characterize intuitive restrictions on preferences that are sufficient for existence. JEL Classification: C78 and D62.
We consider the problem of a monopolist-choosing an optimal nonlinear pricing scheme-facing two c... more We consider the problem of a monopolist-choosing an optimal nonlinear pricing scheme-facing two consumers who can resell some or all of the goods to each other in a secondary market. We suppose that the valuations of the consumers are drawn independently from a continuous distribution. We …nd conditions for the optimum direct mechanism and show that the monopolist can be better o¤ or worse o¤ as compared to the without resale case, depending on the speci…cs of the cost function of the monopolist and the utility functions of the consumers.
Matchings with Aggregate Externalities
Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch ge... more Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence.
Motivated by sponsored search auctions with hard budget constraints given by the advertisers, we ... more Motivated by sponsored search auctions with hard budget constraints given by the advertisers, we study multi-unit auctions of a single item. An important example is a sponsored result slot for a keyword, with many units representing its inventory in a month, say. In this single-item multi-unit auction, each bidder has a private value for each unit, and a private budget which is the total amount of money she can spend in the auction. A recent impossibility result [Dobzinski et al., FOCS'08] precludes the existence of a truthful mechanism with Paretooptimal allocations in this important setting. We propose Sort-Cut, a mechanism which does the next best thing from the auctioneer's point of view, that we term semi-truthful. While we are unable to give a complete characterization of equilibria for our mechanism, we prove that some equilibrium of the proposed mechanism optimizes the revenue over all Pareto-optimal mechanisms, and that this equilibrium is the unique one resulting from a natural rational bidding strategy (where every losing bidder bids at least her true value). Perhaps even more significantly, we show that the revenue of every equilibrium of our mechanism differs by at most the budget of one bidder from the optimum revenue (under some mild assumptions).
This thesis consists of three chapters. In the first chapter, we consider coalition formation gam... more This thesis consists of three chapters. In the first chapter, we consider coalition formation games with externalities. A natural extension of superadditivity is not sufficient to imply that the grand coalition is efficient when externalities are present. We provide a condition, analogous to convexity, that is sufficient for the grand coalition to be efficient and show that this also implies that the (appropriately defined) core is nonempty. Moreover, we propose a mechanism which implements the most efficient partition for all coalition ...
We consider the problem of a monopolisti choosing an optimal nonlinear pricing schemei facing two... more We consider the problem of a monopolisti choosing an optimal nonlinear pricing schemei facing two consumers who can resell some or all of the goods to each other in a secondary market. We suppose that the valuations of the consumers are drawn independently from a continuous distribution. We find conditions for the optimum direct mechanism and show that the monopolist can be better off or worse off as compared to the without resale case, depending on the specifics of the cost function of the monopolist and ...
Journal of Mathematical Economics, Sep 20, 2009
We study first-price auctions in a model with asymmetric, independent private values. Asymmetries... more We study first-price auctions in a model with asymmetric, independent private values. Asymmetries lead to inefficient allocations, thereby creating a motive for resale after the auction is over. In our model, resale takes place via monopoly pricing—the winner of the auction makes a take-it-or-leave-it offer to the loser. Our goal is to compare equilibria of the first-price auction without resale (FPA) with those of the first-price auction with resale (FPAR). For the three major families of distributions for which equilibria of the FPA are ...
A natural,extension,of superadditivity,is not su¢ cient to imply that the grand,coalition is e¢ c... more A natural,extension,of superadditivity,is not su¢ cient to imply that the grand,coalition is e¢ cient when,externalities are present. We provide a con- dition –analogous,to convexity–that,is su¢ cient for the grand coalition to be e¢ cient and show,that this also implies that the (appropriately de…ned) core is nonempty. Moreover, we propose a mechanism which implements the most e¢ cient partition for all coalition formation,games,and characterize the payo¤ division of the mechanism. JEL Classi…cation Numbers: C71, C72, D62 Keywords: Coalition formation, externalities, partition function games, Shapley value, implementation.
International Journal of Game Theory, Nov 1, 2008
In many matching problems, it is natural to consider that agents may have preferences not only ov... more In many matching problems, it is natural to consider that agents may have preferences not only over the set of potential partners but also over what other matches occur. Once such externalities are considered, the set of stable matchings will depend on what agents believe will happen if they deviate. In this paper, we introduce endogenously generated beliefs (which depend on the preferences). We introduce a particular notion of endogenous beliefs, called sophisticated expectations, and show that with these beliefs, ...
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Papers by Isa Emin Hafalir