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Voting and Lottery Drafts as Efficient Public Goods Mechanisms
, 1993
"... This paper characterizes interim efficient mechanisms for public good production and cost allocation in a twotype environment with risk neutral, quasilinear preferences and fixed size projects, where the distribution of the private good, as well as the public goods decision, affects social welfare ..."
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Cited by 13 (0 self)
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This paper characterizes interim efficient mechanisms for public good production and cost allocation in a twotype environment with risk neutral, quasilinear preferences and fixed size projects, where the distribution of the private good, as well as the public goods decision, affects social welfare. An efficient public good decision can always be accomplished by a majority voting scheme, where the number of “YES ” votes required depends on the welfare weights in a simple way. The results are shown to have a natural geometry and an intuitive interpretation. We also extend these results to allow for restrictions on feasible transfer rules, ranging from the traditional unlimited transfers to the extreme case of no transfers. For a range of welfare weights, an optimal scheme is a twostage procedure which combines a voting stage with a second stage where an evenchance lottery is used to determine who pays. We call this the “lottery draft mechanism”. Since such a costsharing scheme does not require transfers, it follows that in many cases transfers are not necessary to achieve the optimal allocation. For other ranges of welfare weights the second stage is more complicated, but the voting stage remains the same. If transfers are completely infeasible, randomized voting rules may be optimal. The paper also provides a geometric characterization of the effects of voluntary participation constraints.
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 10 (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’
Optimal dynamic mechanism design with Deadlines
, 2009
"... A dynamic mechanism design problem with multidimensional private information is studied. There is one object and two buyers who arrive in two different periods. In addition to his privately known valuation, the first buyer also has a privately known deadline for purchasing the object. The seller w ..."
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Cited by 5 (0 self)
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A dynamic mechanism design problem with multidimensional private information is studied. There is one object and two buyers who arrive in two different periods. In addition to his privately known valuation, the first buyer also has a privately known deadline for purchasing the object. The seller wants to maximize revenue. Depending on the type distribution, the incentive compatibility constraint for the deadline may or may not be binding in the optimal mechanism. Sufficient conditions on the type distribution and examples are given for either case. An optimal mechanism for the binding case is derived. It can be implemented by a fixed price in period one and an asymmetric auction in period two. The asymmetry prevails even if the valuations of both buyers are identically distributed. In order to prevent buyer one from buying in the first period when his deadline is two, the seller sets a reserve price that is lower than in the classical (Myerson, 1981) optimal auction and gives him a (nonlinear) bonus. The bonus leads to robust bunching at the top of the typespace. The optimal mechanism can be characterized in terms of generalized virtual valuations which depend endogenously on the allocation rule.
BAYESIAN AND DOMINANT STRATEGY IMPLEMENTATION IN THE INDEPENDENT PRIVATE VALUES MODEL
"... Abstract. We prove—in the standard independent privatevalues model—that the outcome, in terms of expected probabilities of trade and expected transfers, of any Bayesian mechanism, can also be obtained with a dominantstrategy mechanism. Key words: Independent private values, incentive compatibility ..."
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Abstract. We prove—in the standard independent privatevalues model—that the outcome, in terms of expected probabilities of trade and expected transfers, of any Bayesian mechanism, can also be obtained with a dominantstrategy mechanism. Key words: Independent private values, incentive compatibility, Bayesian implementations, dominantstrategy implementation, adverse selection, bilateral trade, mechanism design. 1.
An AuctionTheoretic Modeling of Production Scheduling to Achieve Distributed Decision Making
, 1999
"... Most existing methods for scheduling are based on centralized or hierarchical decision making using monolithic models. In this study, we investigate a new generation of scheduling methods based on a distributed and locally autonomous decision structure. Specifically, we propose a decision structure ..."
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Cited by 3 (0 self)
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Most existing methods for scheduling are based on centralized or hierarchical decision making using monolithic models. In this study, we investigate a new generation of scheduling methods based on a distributed and locally autonomous decision structure. Specifically, we propose a decision structure based on auction theory. The basic idea is to localize and distribute the functionality of scheduling, leaving the complexity of operational decisions to local decision makers, while maintaining a simple and generic central coordination mechanism. The proposed structure allows local decision makers to make their decisions dynamically and independently according to changes in their local environments. A central coordination mechanism then makes resource allocation based on an iterative auction process using information obtained from local decision makers. We propose following research endeavors: ffl We will study the decomposition of monolithic optimization models which provides the basis for...
The Simple Economics of Approximately Optimal Auctions Arvix
, 2012
"... The intuition that profit is optimized by maximizing marginal revenue is a guiding principle in microeconomics. In the classical auction theory for agents with quasilinearutility and singledimensional preferences, Bulow and Roberts (1989) show that the optimal auction of Myerson (1981) is in fact o ..."
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Cited by 2 (1 self)
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The intuition that profit is optimized by maximizing marginal revenue is a guiding principle in microeconomics. In the classical auction theory for agents with quasilinearutility and singledimensional preferences, Bulow and Roberts (1989) show that the optimal auction of Myerson (1981) is in fact optimizing marginal revenue. In particular Myerson’s virtual values are exactly the derivative of an appropriate revenue curve. Thispaperconsidersmechanismdesigninenvironmentswheretheagentshavemultidimensional and nonlinear preferences. Understanding good auctions for these environments is considered to be the main challenge in Bayesian optimal mechanism design. In these environments maximizing marginal revenue may not be optimal, and furthermore, there is sometimes no direct way to implementing the marginal revenue maximization mechanism. Our contributions are three fold: we characterize the settings for which marginal revenue maximization is optimal, we give simple procedures for implementing marginal revenue maximization in general, and we show that marginal revenue maximization is approximately optimal. Our approximation factor smoothly degrades in a term that quantifies how far the environment is from an ideal one (i.e.,
Pure Strategy Equilibria of Multidimensional and NonMonotonic Auctions
, 2004
"... We give necessary and sufficient conditions for the existence of symmetric equilibrium without ties in common values auctions, with multidimensional independent types and no monotonic assumptions. When the conditions are not satisfied, we are still able to prove the existence of pure strategy equili ..."
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We give necessary and sufficient conditions for the existence of symmetric equilibrium without ties in common values auctions, with multidimensional independent types and no monotonic assumptions. When the conditions are not satisfied, we are still able to prove the existence of pure strategy equilibrium with an exogenous and explicit tie breaking mechanism. As a basis for these results, we obtain a characterization lemma that is valid under a general setting, that includes nonindependent types, asymmetrical utilities and any attitude towards risk. Such characterization gives a basis for an intuitive interpretation for the behavior of the bidder: to bid in order to equalize the marginal benefit and the marginal cost of bidding.
Implementation of Reduced Form Mechanisms: A Simple Approach and a New Characterization
, 2012
"... We provide a new characterization of implementability of reduced form mechanisms in terms of straightforward secondorder stochastic dominance. In addition, we present a simple proof of Matthews’ (1984) conjecture, proved by Border (1991), on implementability. ..."
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We provide a new characterization of implementability of reduced form mechanisms in terms of straightforward secondorder stochastic dominance. In addition, we present a simple proof of Matthews’ (1984) conjecture, proved by Border (1991), on implementability.
Proceedings Article PriorIndependent Auctions for RiskAverse Agents
"... We study simple and approximately optimal auctions for agents with a particular form of riskaverse preferences. We show that, for symmetric agents, the optimal revenue (given a prior distribution over the agent preferences) can be approximated by the firstprice auction (which is prior independent) ..."
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We study simple and approximately optimal auctions for agents with a particular form of riskaverse preferences. We show that, for symmetric agents, the optimal revenue (given a prior distribution over the agent preferences) can be approximated by the firstprice auction (which is prior independent), and, for asymmetric agents, the optimal revenue can be approximated by an auction with simple form. These results are based on two technical methods. The first is for upperbounding the revenue from a riskaverse agent. The second gives a payment identity for mechanisms with payyourbid semantics.
Abstract
"... Valiant’s theory of holographic algorithms is a novel methodology to achieve exponential speedups in computation. A fundamental parameter in holographic algorithms is the dimension of the linear basis vectors. We completely resolve the problem of the power of higher dimensional bases. We prove that ..."
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Valiant’s theory of holographic algorithms is a novel methodology to achieve exponential speedups in computation. A fundamental parameter in holographic algorithms is the dimension of the linear basis vectors. We completely resolve the problem of the power of higher dimensional bases. We prove that 2dimensional bases are universal for holographic algorithms. 1