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14
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.
Multiunit auctions with budget limits
 In Proc. of the 49th Annual Symposium on Foundations of Computer Science (FOCS
, 2008
"... We study multiunit auctions where the bidders have a budget constraint, a situation very common in practice that has received very little attention in the auction theory literature. Our main result is an impossibility: there are no incentivecompatible auctions that always produce a Paretooptimal ..."
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Cited by 35 (5 self)
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We study multiunit auctions where the bidders have a budget constraint, a situation very common in practice that has received very little attention in the auction theory literature. Our main result is an impossibility: there are no incentivecompatible auctions that always produce a Paretooptimal allocation. We also obtain some surprising positive results for certain special cases. 1
Bayesian Optimal Auctions via Multi to Singleagent Reduction
, 1203
"... We study an abstract optimal auction problem for a single good or service. This problem includes environments where agents have budgets, risk preferences, or multidimensional preferences over several possible configurations of the good (furthermore, it allows an agent’s budget and risk preference t ..."
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Cited by 9 (3 self)
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We study an abstract optimal auction problem for a single good or service. This problem includes environments where agents have budgets, risk preferences, or multidimensional preferences over several possible configurations of the good (furthermore, it allows an agent’s budget and risk preference to be known only privately to the agent). These are the main challenge areas for auction theory. A singleagent problem is to optimize a given objective subject to a constraint on the maximum probability with which each type is allocated, a.k.a., an allocation rule. Our approach is a reduction from multiagent mechanism design problem to collection of singleagent problems. We focus on maximizing revenue, but our results can be applied to other objectives (e.g., welfare). An optimal multiagent mechanism can be computed by a linear/convex program on interim allocation rules by simultaneously optimizing several singleagent mechanisms subject to joint feasibility of the allocation rules. For singleunit auctions, Border (1991) showed that the space of all jointly feasible interim allocation rules for n agents is a Ddimensional convex polytope which can be specified by 2D linear constraints, where D is the total number of all agents’
Incentive compatible budget elicitation in multiunit auctions
 In Proceedings of the Annual ACMSIAM Symposium on Discrete Algorithms (SODA
, 2010
"... In this paper, we consider the problem of designing incentive compatible auctions for multiple (homogeneous) units of a good, when bidders have private valuations and private budget constraints. When only the valuations are private and the budgets are public, Dobzinski et al [8] show that the adapti ..."
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Cited by 8 (3 self)
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In this paper, we consider the problem of designing incentive compatible auctions for multiple (homogeneous) units of a good, when bidders have private valuations and private budget constraints. When only the valuations are private and the budgets are public, Dobzinski et al [8] show that the adaptive clinching auction is the unique incentivecompatible auction achieving Paretooptimality. They further show that this auction is not truthful with private budgets, so that there is no deterministic Paretooptimal auction with private budgets. Our main contribution is to show the following Budget Monotonicity property of this auction: When there is only one infinitely divisible good, a bidder cannot improve her utility by reporting a budget smaller than the truth. This implies that the adaptive clinching auction is incentive
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
A note on the incompatibility of strategyproofness and paretooptimality in quasilinear settings with public budget constraints
 Abstract in the Proceedings of the 7th Workshop on Internet and Network Economics (WINE’11
"... We study the problem of allocating multiple identical items that may be complements to budgetconstrained bidders with private values. We show that there does not exist a deterministic mechanism that is individually rational, strategyproof, Paretoefficient, and that does not make positive transfer ..."
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Cited by 2 (1 self)
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We study the problem of allocating multiple identical items that may be complements to budgetconstrained bidders with private values. We show that there does not exist a deterministic mechanism that is individually rational, strategyproof, Paretoefficient, and that does not make positive transfers. This is true even if there are only two players, two items, and the budgets are common knowledge. The same impossibility naturally extends to more abstract social choice settings with an arbitrary outcome set, assuming players with quasilinear utilities and public budget limits. Thus, the case of infinite budgets (in which the VCG mechanism satisfies all these properties) is really the exception. JEL Classification Numbers:
Strong Activity Rules for Iterative Combinatorial Auctions
"... Activity rules have emerged in recent years as an important aspect of practical auction design. The role of an activity rule in an iterative auction is to suppress strategic behavior by bidders and promote simple, continual, meaningful bidding and thus, price discovery. These rules find application ..."
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Cited by 2 (0 self)
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Activity rules have emerged in recent years as an important aspect of practical auction design. The role of an activity rule in an iterative auction is to suppress strategic behavior by bidders and promote simple, continual, meaningful bidding and thus, price discovery. These rules find application in the design of iterative combinatorial auctions for real world scenarios, for example in spectrum auctions, in airline landing slot auctions, and in procurement auctions. We introduce the notion of strong activity rules, which allow simple, consistent bidding strategies while precluding all behaviors that cannot be rationalized in this way. We design such a rule for auctions with budgetconstrained bidders, i.e., bidders with valuations for resources that are greater than their ability to pay. Such bidders are of practical importance in many market environments, and hindered from bidding in a simple and consistent way by the commonly used revealedpreference activity rule, which is too strong in such an environment. We consider issues of complexity, and provide two useful forms of information feedback to guide bidders in meeting strong activity rules. As a special case, we derive a strong activity rule for non budgetconstrained bidders. The ultimate choice of activity rule must depend, in part, on beliefs about the types of bidders likely to participate in an auction event because one cannot have a rule that is simultaneously strong for both budgetconstrained bidders and quasilinear bidders.
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.
Revenue Comparisons for Auctions when Bidders Have Arbitrary Types
, 2004
"... This paper develops a methodology for characterizing expected revenue from auctions in which bidders’ types come from an arbitrary distribution. In particular, types may be multidimensional, and there may be mass points in the distribution. One application extends existing revenue equivalence resul ..."
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Cited by 1 (1 self)
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This paper develops a methodology for characterizing expected revenue from auctions in which bidders’ types come from an arbitrary distribution. In particular, types may be multidimensional, and there may be mass points in the distribution. One application extends existing revenue equivalence results. Another application shows that firstprice auctions yield higher expected revenue than secondprice auctions when bidders are risk averse and/or face financial constraints. This revenue ranking also extends to riskaverse bidders with general forms of nonexpected utility preferences.
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.