Multi-Dimensional and Non-Linear Mechanism Design and Approximation I
summary
Claims a modular route from single-agent solutions to multi-agent auctions using a ex-ante reduction (solve best single-player mechanism for each serve-probability) and a more general interim reduction (constraints on the whole interim allocation). Proves revenue equals marginal revenue when revenue linearity holds, yielding a marginal-revenue auction: map types to quantiles, compute marginal revenues, serve to maximize sum. Examples: iid uniform [0,1]^2 (sell favorite color, second-price-with-reserve, reserve = sqrt(1/3)); common budgets (all-pay with reserve and top ironing). Gives a 1.58 approximation from posted uniform prices.
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chapters (10)
- 0:00Intro
- 1:29Example Results Statements
- 8:07Multi-to Single-agent Reductions
- 14:55Ex ante Pricing: Public Budget
- 20:45Unit-demand Preferences
- 28:41Quantile and Allocation Rules
- 40:52Interim Pricing: Examples
- 45:50Unit Demand Example is Revenue Linear
- 49:08Marginal Revenue
- 58:07Optimal Multi-agent Mechanisms
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