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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 11 (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’
WEAK CARTELS AND COLLUSIONPROOF AUCTIONS
"... Abstract. We study collusion in a large class of privatevalue auctions by cartels whose members cannot exchange monetary transfers among themselves (i.e., weak cartels). We provide a complete characterization of outcomes that are implementable in the presence of weak cartels, and identify optimal c ..."
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Abstract. We study collusion in a large class of privatevalue auctions by cartels whose members cannot exchange monetary transfers among themselves (i.e., weak cartels). We provide a complete characterization of outcomes that are implementable in the presence of weak cartels, and identify optimal collusionproof auctions for symmetric value distributions. When the density is singlepeaked, the optimal collusionproof auction can be implemented by a procedure that combines a secondprice auction with a sequential oneonone negotiation.
SYMMETRIC AUCTIONS
, 2013
"... ABSTRACT. Realworld auctions are often restricted to being symmetric (anonymous and nondiscriminatory) due to practical or legal constraints. We examine when this restriction prevents a seller from achieving his objectives. In an independent private value setting with heterogenous buyers, we charac ..."
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ABSTRACT. Realworld auctions are often restricted to being symmetric (anonymous and nondiscriminatory) due to practical or legal constraints. We examine when this restriction prevents a seller from achieving his objectives. In an independent private value setting with heterogenous buyers, we characterize the set of incentive compatible and individually rational outcomes that can be implemented via a symmetric auction. Our characterization shows that symmetric auctions can yield a large variety of discriminatory outcomes such as revenue maximization and affirmative action. We also characterize the set of implementable outcomes when individual rationality holds in an expost rather than an interim sense. This additional requirement may prevent the seller from maximizing revenue.
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.
Public Projects, Boolean Functions, and the Borders of Border’s Theorem
, 2015
"... Border’s theorem gives an intuitive linear characterization of the feasible interim allocation rules of a Bayesian singleitem environment, and it has several applications in economic and algorithmic mechanism design. All known generalizations of Border’s theorem either restrict attention to relat ..."
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Border’s theorem gives an intuitive linear characterization of the feasible interim allocation rules of a Bayesian singleitem environment, and it has several applications in economic and algorithmic mechanism design. All known generalizations of Border’s theorem either restrict attention to relatively simple settings, or resort to approximation. This paper identifies a complexitytheoretic barrier that indicates, assuming standard complexity class separations, that Border’s theorem cannot be extended significantly beyond the stateoftheart. We also identify a surprisingly tight connection between Myerson’s optimal auction theory, when applied to public project settings, and some fundamental results in the analysis of Boolean functions. 1