Robustness and Separation in Multidimensional Mechanism Design
summary
Claim: when only marginal type distributions are known and correlation is unknown, the worst-case revenue guarantee equals the sum of single-item optimal revenues, so it is optimal to sell goods separately. Proof constructs a specific worst-case joint distribution and certificates via LP duality construction using nonnegative reweighting factors (gammas) that pin down joint probabilities. Proof covers finite type spaces (extends by approximation) and yields a tight R* bound; counterexamples show naive positive-correlation arguments can fail.
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chapters (17)
- 0:00Intro
- 0:25Multidimensional screening is hard
- 3:21Multidimensional screening is important
- 4:09A robust approach
- 6:21A general separation theorem
- 9:09Screening problems A screening problem consists of
- 10:38Worst-case criterion
- 11:23Applications
- 13:53Non-proof: Independent distributions
- 15:04Non-proof: Comonotonic distribution
- 17:00Counterexample with comonotonic distribution Discrete example (can make continuous)
- 19:31Worst-case distribution in example
- 20:06Real proof: Outline
- 21:23Which constraints to use?
- 23:08Multipliers in component problems
- 26:52Finding the joint multipliers
- 31:10Summary