## Optimal auction in a multidimensional worldCenter for Mathematical Studies in Economics and Management Science, Northwestern University, 2000 - Auctions - 44 pages |

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additively separable Armstrong attribute bundle auction setting auction theory Barbarika bidder-types bidder's expected payoff bidder's payoff bidder's type bids binding IC constraint calculate compact continuously differentiable convex Corollary denote density function divergence theorem Envelope Theorem Equation 17 equilibrium expected payoff equivalent Exclusion Principle follows greedy algorithm hazard rate implies incentive-compatibility constraint independent private value induced type Jean Tirole Lemma level set Mark Armstrong maximizes the seller's mechanism p*,q*,s minimum score monotonicity condition multidimensional nonlinear pricing Myerson 15 non-binding nondecreasing nonmonetary bundle nonnegative nonpositive optimal auction design optimal mechanism optimal scoring rule optimizing seller positive measure pricing function private value auction proof Proposition 4.1 proves Claim range regular mechanisms regularity condition reserve price revelation game Rochet scoring-rule auction seller-optimal seller's equilibrium expected seller's expected payoff seller's payoff statistic strictly increasing transaction true preferences type-i vector Vickrey auction virtual utility well-behaved scoring mechanisms winner winner's payoff zero winning probability