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14
Auction Theory: A Guide to the Literature
 JOURNAL OF ECONOMIC SURVEYS
, 1999
"... This paper provides an elementary, nontechnical, survey of auction theory, by introducing and describing some of the critical papers in the subject. (The most important of these are reproduced in a companion book, The Economic Theory of Auctions, Paul Klemperer (ed.), Edward Elgar (pub.), forthco ..."
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Cited by 349 (2 self)
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This paper provides an elementary, nontechnical, survey of auction theory, by introducing and describing some of the critical papers in the subject. (The most important of these are reproduced in a companion book, The Economic Theory of Auctions, Paul Klemperer (ed.), Edward Elgar (pub.), forthcoming.) We begin with the most fundamental concepts, and then introduce the basic analysis of optimal auctions, the revenue equivalence theorem, and marginal revenues. Subsequent sections address riskaversion, affiliation, asymmetries, entry, collusion, multiunit auctions, double auctions, royalties, incentive contracts, and other topics. Appendices contain technical details, some simple worked examples, and a bibliography for each section.
Multiunit auctions with budgetconstrained bidders
 In Proceedings of the 7th ACM Conference on Electronic Commerce
, 2005
"... We study a multiunit auction with multiple bidders, each of whom has a private valuation and a budget. The truthful mechanisms of such an auction are characterized, in the sense that, under standard assumptions, we prove that it is impossible to design a nontrivial truthful auction which allocates ..."
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Cited by 74 (10 self)
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We study a multiunit auction with multiple bidders, each of whom has a private valuation and a budget. The truthful mechanisms of such an auction are characterized, in the sense that, under standard assumptions, we prove that it is impossible to design a nontrivial truthful auction which allocates all units, while we provide the design of an asymptotically revenuemaximizing truthful mechanism which may allocate only some of the units. Our asymptotic parameter is a budget dominance parameter which measures the size of the budget of a single agent relative to the maximum revenue. We discuss the relevance of these results for the design of Internet ad auctions.
Budget constrained auctions with heterogeneous items
 In Proceedings 42nd ACM Symposium on Theory of Computing
, 2010
"... In this paper, we present the first approximation algorithms for the celebrated problem of designing revenue optimal Bayesian incentive compatible auctions when there are multiple (heterogeneous) items and when bidders can have arbitrary demand and budget constraints. Our mechanisms are surprisingly ..."
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Cited by 19 (1 self)
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In this paper, we present the first approximation algorithms for the celebrated problem of designing revenue optimal Bayesian incentive compatible auctions when there are multiple (heterogeneous) items and when bidders can have arbitrary demand and budget constraints. Our mechanisms are surprisingly simple: We show that a sequential allpay mechanism is a 4 approximation to the revenue of the optimal exinterim truthful mechanism with discrete correlated type space for each bidder. We also show that a sequential posted price mechanism is a O(1) approximation to the revenue of the optimal expost truthful mechanism when the type space of each bidder is a product distribution that satisfies the standard hazard rate condition. We further show a logarithmic approximation when the hazard rate condition is removed, and complete the picture by showing that achieving a sublogarithmic approximation, even for regular distributions and one bidder, requires pricing bundles of items. Our results are based on formulating novel LP relaxations for these problems, and developing generic rounding schemes from first principles. We believe this approach will be useful in other Bayesian mechanism design contexts.
SortCut: A ParetoOptimal and SemiTruthful Mechanism for MultiUnit Auctions with BudgetConstrained Bidders
"... Motivated by sponsored search auctions with hard budget constraints given by the advertisers, we study multiunit 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 singleitem multiunit aucti ..."
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Cited by 4 (0 self)
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Motivated by sponsored search auctions with hard budget constraints given by the advertisers, we study multiunit 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 singleitem multiunit 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 SortCut, 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.
Computing With Strategic Agents
, 2005
"... This dissertation studies mechanism design for various combinatorial problems in the presence of strategic agents. A mechanism is an algorithm for allocating a resource among a group of participants, each of which has a privatelyknown value for any particular allocation. A mechanism is truthful if ..."
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Cited by 3 (2 self)
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This dissertation studies mechanism design for various combinatorial problems in the presence of strategic agents. A mechanism is an algorithm for allocating a resource among a group of participants, each of which has a privatelyknown value for any particular allocation. A mechanism is truthful if it is in each participant’s best interest to reveal his private information truthfully regardless of the strategies of the other participants. First, we explore a competitive auction framework for truthful mechanism design in the setting of multiunit auctions, or auctions which sell multiple identical copies of a good. In this framework, the goal is to design a truthful auction whose revenue approximates that of an omniscient auction for any set of bids. We focus on two natural settings — the limited demand setting where bidders desire at most a fixed number of copies and the limited budget setting where bidders can spend at most a fixed amount of money. In the limit demand setting, all prior auctions employed the use of randomization in the computation of the allocation and prices. Randomization
QuasiProportional Mechanisms: Priorfree Revenue Maximization
, 909
"... Abstract. Inspired by Internet ad auction applications, we study the problem of allocating a single item via an auction when bidders place very different values on the item. We formulate this as the problem of priorfree auction and focus on designing a simple mechanism that always allocates the ite ..."
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Cited by 2 (0 self)
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Abstract. Inspired by Internet ad auction applications, we study the problem of allocating a single item via an auction when bidders place very different values on the item. We formulate this as the problem of priorfree auction and focus on designing a simple mechanism that always allocates the item. Rather than designing sophisticated pricing methods like prior literature, we design better allocation methods. In particular, we propose quasiproportional allocation methods in which the probability that an item is allocated to a bidder depends (quasiproportionally) on the bids. We prove that corresponding games for both allpay and winnerspay quasiproportional mechanisms admit pure Nash equilibria and this equilibrium is unique. We also give an algorithm to compute this equilibrium in polynomial time. Further, we show that the revenue of the auctioneer is promisingly high compared to the ultimate, i.e., the highest value of any of the bidders, and show bounds on the revenue of equilibria both analytically, as well as using experiments for specific quasiproportional functions. This is the first known revenue analysis for these natural mechanisms (including the special case of proportional mechanism which is common in network resource allocation problems).
An Ascending MultiItem Auction with Financially Constrained Bidders ∗
, 2008
"... A number of heterogeneous items are to be sold to a group of potential bidders. Every bidder knows his own values over the items and his own budget privately. Due to budget constraint, bidders may not be able to pay up to their values. In such a market, a Walrasian equilibrium usually fails to exist ..."
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Cited by 1 (0 self)
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A number of heterogeneous items are to be sold to a group of potential bidders. Every bidder knows his own values over the items and his own budget privately. Due to budget constraint, bidders may not be able to pay up to their values. In such a market, a Walrasian equilibrium usually fails to exist and also the existing auctions might fail to allocate the items among the bidders. In this paper we first introduce a rationed equilibrium for a market situation with financially constrained bidders. Succeedingly we propose an ascending auction mechanism that always results in an equilibrium allocation and price system. By starting with the reservation price of each item, the auctioneer announces the current prices of the items in each step and the bidders respond with their demand sets at these prices. As long as there is overdemand, the auctioneer adjusts prices upwards for overdemanded items until a price system is reached at which either there is an underdemanded set, or there is neither overdemand nor underdemand anymore. In the latter case the auction stops. In the former case, precisely one item will be sold, the bidder buying the item leaves the auction and the auction continues with the remaining items and the remaining bidders. We prove that the auction finds a rationed equilibrium in a finite number of steps. In addition, we derive various properties of the allocation and price system obtained by the auction.
Persistent Markups in Bidding Markets with Financial Constraints ∗
, 2011
"... This paper studies the impact of financial constraints on the persistency of high markups in a class of markets, including public procurement, known by practitioners as bidding markets. We develop an infinite horizon model in which two firms optimally reinvest working capital and bid for a procureme ..."
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Cited by 1 (1 self)
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This paper studies the impact of financial constraints on the persistency of high markups in a class of markets, including public procurement, known by practitioners as bidding markets. We develop an infinite horizon model in which two firms optimally reinvest working capital and bid for a procurement contract each period. Working capital is constrained by the firm’s cash from previous period and some exogenous cash flow, it is costly and it increases the set of acceptable bids. We argue that the latter is a natural consequence of the presence of progress payments or the existence of moral hazard. We say that the firm is (severely) financially constrained if its working capital is such that only bids (substantially) above production cost are acceptable. We show that markups are positive (high) if and only if one firm is (severely) financially constrained. Our main result is that markups are persistently high because one firm is severely financially constrained most of the time.
Revenue Maximization When Bidders Have Budgets
"... We study the problem of maximizing revenue for auctions with multiple units of a good where bidders have hard budget constraints, first considered in [2]. The revenue obtained by an auction is compared with the optimal omniscient auction had the auctioneer known the private information of all the bi ..."
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We study the problem of maximizing revenue for auctions with multiple units of a good where bidders have hard budget constraints, first considered in [2]. The revenue obtained by an auction is compared with the optimal omniscient auction had the auctioneer known the private information of all the bidders, as in competitive analysis [7]. We show that the revenue of the optimal omniscient auction that sells items at many di#erent prices is within a factor of 2 of the optimal omniscient auction that sells all the items at a single price, implying that our results will carry over to multiple price auctions. We give the first auction for this problem, to the best of our knowledge, that is known to obtain a constant fraction of the optimal revenue when the bidder dominance (the ratio between the maximum contribution of a single bidder in the optimal solution and the revenue of that optimal solution) is large (as high as 2 ). Our auction is also shown to remain truthful if canceled upon not meeting certain criteria. On the negative side, we show that no auction can achieve a guarantee of 2# the revenue of the optimal omniscient multiprice auction. Finally, if the bidder dominance is known in advance and is less than 5.828 , we give an auction mechanism that raises a large constant fraction of the optimal revenue when the bidder dominance is large and is asymptotically close to the optimal omniscient auction as the bidder dominance decreases. We discuss the relevance of these results for related applications.
Bidding Markets with Financial Constraints ∗
, 2013
"... We develop a model of bidding markets with financial constraints a la Che and Gale (1998b) in which two firms optimally choose their budgets. First, we provide an alternative explanation for the dispersion of markups and “money left on the table” across procurement auctions. Interestingly, this expl ..."
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We develop a model of bidding markets with financial constraints a la Che and Gale (1998b) in which two firms optimally choose their budgets. First, we provide an alternative explanation for the dispersion of markups and “money left on the table” across procurement auctions. Interestingly, this explanation does not hinge on significant private information but on differences, both endogenous and exogenous, in the availability of financial resources. Second, we explain why the empirical analysis of the size of markups may be biased downwards or upwards with a bias positively correlated with the availability of financial resources when the researcher assumes that the data are generated by the standard auction model. Third, we show that large concentration and persistent asymmetries in market shares together with occasional leadership reversals can arise as a consequence of the firms internal financial decisions even in the absence of exogenous shocks.