Controlled choice over public schools attempts giving options to parents while maintaining divers... more Controlled choice over public schools attempts giving options to parents while maintaining diversity, often enforced by setting feasibility constraints with hard upper and lower bounds for each student type. We demonstrate that there might not exist assignments that satisfy standard fairness and non-wastefulness properties; whereas constrained non-wasteful assignments which are fair for same type students always exist.
We study dominant strategy implementable direct mechanisms that minimize the expected surplus fro... more We study dominant strategy implementable direct mechanisms that minimize the expected surplus from core deviations. Using incentive compatibility conditions, we formulate the core deviation miminimization problem as a calculus of variations problem and then numerically solve it for some particular cases.
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.
We offer a theoretical and empirical comparison of auctions and negotiated sales. We first build ... more We offer a theoretical and empirical comparison of auctions and negotiated sales. We first build a simple model to show that auctions generate a higher relative price than negotiated sales when demand for the asset is strong, when the asset is more homogeneous, and when the asset attracts buyers with higher valuations. Using data from property sales in Singapore, we
In a setup where a divisible good is to be allocated to a set of bidders with budget constraints,... more In a setup where a divisible good is to be allocated to a set of bidders with budget constraints, we introduce a mechanism in the spirit of the Vickrey auction. In the mechanism we propose, understating budgets or values is weakly dominated. Since the revenue is increasing in budgets and values, all kinds of equilibrium deviations from true valuations turn out to be beneficial to the auctioneer. We also show that ex-post Nash equilibrium of our mechanism is near Pareto optimal in the sense that all full winnersĘĽ values are above all full losersĘĽ values.
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).
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 over the whole matching. Once such externalities are considered, the set of stable matchings will depend on what agents believe will happen if they deviate. Sasaki and Toda (1996, J. of Econ. Theory, 70, 93) have examined the existence of stable matchings when the beliefs are exogenously speci…ed and shown that stable matchings do not always exist. In this paper, we argue that beliefs should be endogenously generated, that is, they should depend on the preferences. We introduce a particular notion of endogenous beliefs, called sophisticated expectations, and show that with these beliefs, stable matchings always exist.
A natural extension of superadditivity is not sufficient to imply that the grand coalition is eff... more 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 characterizes the resulting payoff division.
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 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.
We study equilibria of …rst-and second-price auctions with resale in a model with independent pri... more We study equilibria of …rst-and second-price auctions with resale in a model with independent private values. With asymmetric bidders, the resulting ine¢ciencies create a motive for post-auction trade. In our basic model, resale takes place via monopoly pricing-the winner of the auction makes a take-it-or-leaveit o¤er to the loser after updating his prior beliefs based on his winning. We show that a …rst-price auction with resale has a unique monotonic equilibrium. Our main result is that with resale, the expected revenue from a …rst-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.
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).
Abstract We consider the problem of a monopolisti choosing an optimal nonlinear pricing schemei f... more Abstract 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.
Abstract: We study dominant strategy implementable direct mechanisms that minimize the expected s... more Abstract: We study dominant strategy implementable direct mechanisms that minimize the expected surplus from core deviations. Using incentive compatibility conditions, we formulate the core deviation miminimization problem as a calculus of variations problem and then numerically solve it for some particular cases.
Abstract: We offer a theoretical and empirical comparison of auctions and negotiated sales. We fi... more Abstract: We offer a theoretical and empirical comparison of auctions and negotiated sales. We first build a simple model to show that auctions generate a higher relative price than negotiated sales when demand for the asset is strong, when the asset is more homogeneous, and when the asset attracts buyers with higher valuations.
Abstract We introduce a new mechanism for call auctions which are widely used in stock exchanges.... more Abstract We introduce a new mechanism for call auctions which are widely used in stock exchanges. By incorporating contingent claims (buy stock A, if selling stock B) into the price discovery process, we achieve a higher liquidity in call auctions and lower volatility after opening call auctions. We also show that present call auctions and the proposed mechanism have similar incentive prop'erties. Keywords: Call Auctions, Stock Exchanges, Volatility JEL Codes: G20, D44
A natural extension of superadditivity is not sufficient to imply that the grand coalition is eff... more 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 characterizes the resulting payoff division.
Abstract In many matching problems, it is natural to consider that agents may have preferences no... more Abstract 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).
Abstract: We study first-and second-price auctions with resale in a model with independent privat... more Abstract: We study 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 which, in our model, takes place via monopoly pricing—the winner makes a take-it-or-leave-it offer to the loser. We show (a) a first-price auction with resale has a unique monotonic equilibrium; and (b) with resale, the expected revenue from a first-price auction exceeds that from a second-price auction.
In a setup where a divisible good is to be allocated to a set of bidders with budget constraints,... more In a setup where a divisible good is to be allocated to a set of bidders with budget constraints, we introduce a mechanism in the spirit of the Vickrey auction. In the mechanism we propose, understating budgets or values is weakly dominated. Since the revenue is increasing in budgets and values, all kinds of equilibrium deviations from true valuations turn out to be beneficial to the auctioneer.
Abstract We consider an environment where the sale can take place so early that both the seller a... more Abstract 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.
Controlled choice over public schools attempts giving options to parents while maintaining divers... more Controlled choice over public schools attempts giving options to parents while maintaining diversity, often enforced by setting feasibility constraints with hard upper and lower bounds for each student type. We demonstrate that there might not exist assignments that satisfy standard fairness and non-wastefulness properties; whereas constrained non-wasteful assignments which are fair for same type students always exist.
We study dominant strategy implementable direct mechanisms that minimize the expected surplus fro... more We study dominant strategy implementable direct mechanisms that minimize the expected surplus from core deviations. Using incentive compatibility conditions, we formulate the core deviation miminimization problem as a calculus of variations problem and then numerically solve it for some particular cases.
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.
We offer a theoretical and empirical comparison of auctions and negotiated sales. We first build ... more We offer a theoretical and empirical comparison of auctions and negotiated sales. We first build a simple model to show that auctions generate a higher relative price than negotiated sales when demand for the asset is strong, when the asset is more homogeneous, and when the asset attracts buyers with higher valuations. Using data from property sales in Singapore, we
In a setup where a divisible good is to be allocated to a set of bidders with budget constraints,... more In a setup where a divisible good is to be allocated to a set of bidders with budget constraints, we introduce a mechanism in the spirit of the Vickrey auction. In the mechanism we propose, understating budgets or values is weakly dominated. Since the revenue is increasing in budgets and values, all kinds of equilibrium deviations from true valuations turn out to be beneficial to the auctioneer. We also show that ex-post Nash equilibrium of our mechanism is near Pareto optimal in the sense that all full winnersĘĽ values are above all full losersĘĽ values.
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).
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 over the whole matching. Once such externalities are considered, the set of stable matchings will depend on what agents believe will happen if they deviate. Sasaki and Toda (1996, J. of Econ. Theory, 70, 93) have examined the existence of stable matchings when the beliefs are exogenously speci…ed and shown that stable matchings do not always exist. In this paper, we argue that beliefs should be endogenously generated, that is, they should depend on the preferences. We introduce a particular notion of endogenous beliefs, called sophisticated expectations, and show that with these beliefs, stable matchings always exist.
A natural extension of superadditivity is not sufficient to imply that the grand coalition is eff... more 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 characterizes the resulting payoff division.
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 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.
We study equilibria of …rst-and second-price auctions with resale in a model with independent pri... more We study equilibria of …rst-and second-price auctions with resale in a model with independent private values. With asymmetric bidders, the resulting ine¢ciencies create a motive for post-auction trade. In our basic model, resale takes place via monopoly pricing-the winner of the auction makes a take-it-or-leaveit o¤er to the loser after updating his prior beliefs based on his winning. We show that a …rst-price auction with resale has a unique monotonic equilibrium. Our main result is that with resale, the expected revenue from a …rst-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.
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).
Abstract We consider the problem of a monopolisti choosing an optimal nonlinear pricing schemei f... more Abstract 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.
Abstract: We study dominant strategy implementable direct mechanisms that minimize the expected s... more Abstract: We study dominant strategy implementable direct mechanisms that minimize the expected surplus from core deviations. Using incentive compatibility conditions, we formulate the core deviation miminimization problem as a calculus of variations problem and then numerically solve it for some particular cases.
Abstract: We offer a theoretical and empirical comparison of auctions and negotiated sales. We fi... more Abstract: We offer a theoretical and empirical comparison of auctions and negotiated sales. We first build a simple model to show that auctions generate a higher relative price than negotiated sales when demand for the asset is strong, when the asset is more homogeneous, and when the asset attracts buyers with higher valuations.
Abstract We introduce a new mechanism for call auctions which are widely used in stock exchanges.... more Abstract We introduce a new mechanism for call auctions which are widely used in stock exchanges. By incorporating contingent claims (buy stock A, if selling stock B) into the price discovery process, we achieve a higher liquidity in call auctions and lower volatility after opening call auctions. We also show that present call auctions and the proposed mechanism have similar incentive prop'erties. Keywords: Call Auctions, Stock Exchanges, Volatility JEL Codes: G20, D44
A natural extension of superadditivity is not sufficient to imply that the grand coalition is eff... more 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 characterizes the resulting payoff division.
Abstract In many matching problems, it is natural to consider that agents may have preferences no... more Abstract 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).
Abstract: We study first-and second-price auctions with resale in a model with independent privat... more Abstract: We study 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 which, in our model, takes place via monopoly pricing—the winner makes a take-it-or-leave-it offer to the loser. We show (a) a first-price auction with resale has a unique monotonic equilibrium; and (b) with resale, the expected revenue from a first-price auction exceeds that from a second-price auction.
In a setup where a divisible good is to be allocated to a set of bidders with budget constraints,... more In a setup where a divisible good is to be allocated to a set of bidders with budget constraints, we introduce a mechanism in the spirit of the Vickrey auction. In the mechanism we propose, understating budgets or values is weakly dominated. Since the revenue is increasing in budgets and values, all kinds of equilibrium deviations from true valuations turn out to be beneficial to the auctioneer.
Abstract We consider an environment where the sale can take place so early that both the seller a... more Abstract 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.
Uploads
Papers by Isa Hafalir