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27
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
Optimal Auctions with Financially Constrained Bidders
, 2009
"... We consider an environment where potential exante symmetric buyers of an indivisible good have liquidity constraints, in that they cannot pay more than their ‘budget’ regardless of their valuation. A buyer’s valuation for the good as well as her budget are her private information. We derive the sym ..."
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Cited by 21 (3 self)
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We consider an environment where potential exante symmetric buyers of an indivisible good have liquidity constraints, in that they cannot pay more than their ‘budget’ regardless of their valuation. A buyer’s valuation for the good as well as her budget are her private information. We derive the symmetric constrainedefficient and revenue maximizing auctions for this setting. In general, the optimal auction requires ‘pooling’ both at the top and in the middle despite the maintained assumption of a monotone hazard rate. Further, the auctioneer will never find it desirable to subsidize bidders with low budgets.
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.
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
Bayesian Mechanism Design for BudgetConstrained Agents
, 2011
"... We study Bayesian mechanism design problems in settings where agents have budgets. Specifically, an agent’s utility for an outcome is given by his value for the outcome minus any payment he makes to the mechanism, as long as the payment is below his budget, and is negative infinity otherwise. This d ..."
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Cited by 3 (0 self)
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We study Bayesian mechanism design problems in settings where agents have budgets. Specifically, an agent’s utility for an outcome is given by his value for the outcome minus any payment he makes to the mechanism, as long as the payment is below his budget, and is negative infinity otherwise. This discontinuity in the utility function presents a significant challenge in the design of good mechanisms, and classical “unconstrained ” mechanisms fail to work in settings with budgets. The goal of this paper is to develop general reductions from budgetconstrained Bayesian MD to unconstrained Bayesian MD with small loss in performance. We consider this question in the context of the two most wellstudied objectives in mechanism design—social welfare and revenue—and present constant factor approximations in a number of settings. Some of our results extend to settings where budgets are private and agents need to be incentivized to reveal them truthfully.
Strategic Betting for Competitive Agents
"... In many multiagent settings, each agent’s goal is to come out ahead of the other agents on some metric, such as the currency obtained by the agent. In such settings, it is not appropriate for an agent to try to maximize its expected score on the metric; rather, the agent should maximize its expected ..."
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Cited by 2 (1 self)
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In many multiagent settings, each agent’s goal is to come out ahead of the other agents on some metric, such as the currency obtained by the agent. In such settings, it is not appropriate for an agent to try to maximize its expected score on the metric; rather, the agent should maximize its expected probability of winning. In principle, given this objective, the game can be solved using gametheoretic techniques. However, most games of interest are far too large and complex to solve exactly. To get some intuition as to what an optimal strategy in such games should look like, we introduce a simplified game that captures some of their key aspects, and solve it (and several variants) exactly. Specifically, the basic game that we study is the following: each agent i chooses a lottery over nonnegative numbers whose expectation is equal to its budget bi. The agent with the highest realized outcome wins (and agents only care about winning). We show that there is a unique symmetric equilibrium when budgets are equal. We proceed to study and solve extensions, including settings where agents must obtain a minimum outcome to win; where agents choose their budgets (at a cost); and where budgets are private information.
JeanJacques Laffont: A Look Back
 Journal of the European Economic Association
, 2004
"... JeanJacques Laffont, economist extraordinaire and visionary founder of the Institut de l’Economie Industrielle ( IDEI) in Toulouse, died at his home in Colomiers on May 1 after a valiant battle against cancer. He was fiftyseven years old. Laffont is remarkable for having had three distinct profess ..."
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Cited by 2 (0 self)
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JeanJacques Laffont, economist extraordinaire and visionary founder of the Institut de l’Economie Industrielle ( IDEI) in Toulouse, died at his home in Colomiers on May 1 after a valiant battle against cancer. He was fiftyseven years old. Laffont is remarkable for having had three distinct professional identities and for performing at the very highest level in all of them. First, he was one of the great economists of our time. He was instrumental in transforming public economics, regulatory economics, and the economics of organizations into fields of study that put primary emphasis on conflicts in incentives. In a dozen books and many scores of articles, he examined these conflicts, which arise when the objectives of a society, industry, or organization differ from those of the agents—e.g., people or firms—who belong to them. Second, as an institution builder, Laffont assembled a formidable array of economic talent at IDEI, now one of the finest educational and research groups in the world. Somehow Laffont overcame the gravitational attraction of Paris and brought this talent to Toulouse, then a relative backwater. On a continent where universities are