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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 ..."
Abstract

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’
On the equivalence of bayesian and dominant strategy implementation’, Econometrica 81(1
, 2013
"... We consider a standard social choice environment with linear utility and onedimensional types. We show by counterexample that, when there are at least three physical alternatives, BayesNash Incentive Compatibility (BIC) and Dominant Strategy Incentive Compatibility (DIC) need no longer be equivale ..."
Abstract

Cited by 2 (0 self)
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We consider a standard social choice environment with linear utility and onedimensional types. We show by counterexample that, when there are at least three physical alternatives, BayesNash Incentive Compatibility (BIC) and Dominant Strategy Incentive Compatibility (DIC) need no longer be equivalent. The example with three alternatives is minimal since we do obtain a general equivalence result for settings with only two social alternatives. Our negative result does not mathematically contradict the Manelli and Vincent [2010] equivalence obtained in a oneobject auction setting, but it shows that BICDIC equivalence is only valid in restrictive environments. Our insights are based on mathematical results about the existence of monotone measures with given monotone marginals. 1
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. 1 ..."
Abstract
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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. 1