Multi-Dimensional Optimal Mechanism Design:
Part 5
December 4, 2015
1
A multi-dimensional analog of Myerson's theory
1.1
A structural characterization of optimal mechanisms
We have previously stated that under certain conditions revenue-maximizing
optimal
Multi-Dimensional Optimal Mechanism Design:
Part 4
December 4, 2015
1
A multi-dimensional analog of Myerson's theory
1.1
Border's theorem and its extension
Border's Theorem [5] characterizes interim feasibility for single-item auction
environments. To der
Multi-Dimensional Optimal Mechanism Design:
Part 6
December 4, 2015
1
1.1
The complexity of optimal mechanism design
Main result
In April 2013, [12] proved that a general revenue-optimal auction in multi-item
settings cannot be found and implemented compu
Multi-Dimensional Optimal Mechanism Design:
Part 3
December 4, 2015
1
A multi-dimensional analog of Myerson's theory
1.1
Reduced-form auctions
Let (x, p) be a direct-revealation mechanism where x is the (ex-post) allocation
rule and p is the payment rule.
Multi-Dimensional Optimal Mechanism Design:
Part 10
December 4, 2015
1
Improved approximations
1.1
Multiple bidders
In January 2015 [10] provided a lookahead reduction for the case of many additive bidders. Applying the single-buyer mechanisms from [9] wi
Multi-Dimensional Optimal Mechanism Design:
Part 8
December 4, 2015
1
Approximately optimal multi-dimensional mechanisms
In this part we're going to focus mostly on results, without getting into much
details. We are going to briey mention the important te
Multi-Dimensional Optimal Mechanism Design:
Part 7
December 4, 2015
1
1.1
The complexity of optimal mechanism design
Proof outline
To prove this result, they narrow into a family of single-bidder instances for
which there is a unique optimal BIC, IR, dire
Multi-Dimensional Optimal Mechanism Design:
Part 11
December 4, 2015
1
Approximately optimal multi-dimensional mechanisms
1.1
Correlated items
The above process is highly specialized to additive bidders and independently
distributed items. Therefore, an o
Multi-Dimensional Optimal Mechanism Design:
Part 2
December 4, 2015
1
A multi-dimensional analog of Myerson's theory
The goal of this part is to present a multi-dimensional analog of Myerson's
theory of revenue-maximizing optimal auctions. Most of the ide
Multi-Dimensional Optimal Mechanism Design:
Part 9
December 4, 2015
1
1.1
Approximately optimal
Tight bounds
One Year later (2013), [8] showed tight bounds on approximation of the optimal revenue for selling
one additive buyer.
k
independently distributed
Multi-Dimensional Optimal Mechanism Design:
Part 1
December 4, 2015
1
Introduction
This work deals with the objective of maximizing revenue in multi-dimensional
mechanism design. As we've seen in the lecture on revenue, Myerson [6] gave
a complete solutio
1
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