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**11 - 13**of**13**### Multi-Item Auctions Defying Intuition?

, 2013

"... The best way to sell n items to a buyer who values each of them independently and uniformly randomly in [c, c+ 1] is to bundle them together, as long as c is large enough. Still, for any c, the grand bundling mechanism is never optimal for large enough n, despite the sharp concentration of the buyer ..."

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The best way to sell n items to a buyer who values each of them independently and uniformly randomly in [c, c+ 1] is to bundle them together, as long as c is large enough. Still, for any c, the grand bundling mechanism is never optimal for large enough n, despite the sharp concentration of the buyer’s total value for the items as n grows. Optimal multi-item mechanisms are rife with unintuitive properties, making multi-item generalizations of Myerson’s celebrated mechanism a daunting task. We survey recent work on the structure and computational complexity of revenue-optimal multi-item mechanisms, providing structural as well as algorithmic generalizations of Myerson’s result to multi-item settings.

### Near-Optimal and Robust Mechanism Design for Covering Problems with Correlated Players

, 2013

"... We consider the problem of designing incentive-compatible, ex-post individually rational (IR) mechanisms for covering problems in the Bayesian setting, where players ’ types are drawn from an underlying distribution and may be correlated, and the goal is to minimize the expected total payment made ..."

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We consider the problem of designing incentive-compatible, ex-post individually rational (IR) mechanisms for covering problems in the Bayesian setting, where players ’ types are drawn from an underlying distribution and may be correlated, and the goal is to minimize the expected total payment made by the mechanism. We formulate a notion of incentive compatibility (IC) that we call robust Bayesian IC (robust BIC) that is substantially more robust than BIC, and develop black-box reductions from robust-BIC mechanism design to algorithm design. For single-dimensional settings, this black-box reduction applies even when we only have an LP-relative approximation algorithm for the algorithmic problem. Thus, we obtain near-optimal mechanisms for various covering settings including single-dimensional covering problems, multi-item procurement auctions, and multidimensional facility location.

### Optimal Auctions via the Multiplicative Weight Method

, 2013

"... We show that the multiplicative weight update method provides a simple recipe for designing and analyzing optimal Bayesian Incentive Compatible (BIC) auctions, and reduces the time complexity of the problem to pseudo-polynomial in parameters that depend on single agent instead of depending on the si ..."

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We show that the multiplicative weight update method provides a simple recipe for designing and analyzing optimal Bayesian Incentive Compatible (BIC) auctions, and reduces the time complexity of the problem to pseudo-polynomial in parameters that depend on single agent instead of depending on the size of the joint type space. We use this framework to design computationally efficient optimal auctions that satisfy ex-post Individual Rationality in the presence of constraints such as (hard, private) budgets and envy-freeness. We also design optimal auctions when buyers and a seller’s utility functions are non-linear. Scenarios with such functions include (a) auctions with “quitting rights”, (b) cost to borrow money beyond budget, (c) a seller’s and buyers ’ risk aversion. Finally, we show how our framework also yields optimal auctions for variety of auction settings considered in [20, 2, 11, 12, 13], albeit with pseudo-polynomial running times.