A Simplified Analysis of the Ascending Auction to Sell a Matroid Base
Britta Peis, Niklas Rieken
TL;DR
This paper provides a simplified analysis of an ascending auction mechanism for selling a matroid base at Vickrey prices, making the economic efficiency proof more accessible using basic matroid theorems.
Contribution
It introduces a streamlined proof of the auction's efficiency and pricing properties, reducing reliance on complex arguments.
Findings
Proves the auction's economic efficiency with simpler methods
Shows the auction achieves Vickrey prices for welfare-maximizing bases
Uses basic matroid theorems to simplify analysis
Abstract
We give a simpler analysis of the ascending auction of Bikhchandani, de Vries, Schummer, and Vohra to sell a welfare-maximizing base of a matroid at Vickrey prices. The new proofs for economic efficiency and the charge of Vickrey prices only require a few matroid folklore theorems, therefore shortening the analysis of the design goals of the auction significantly.
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Taxonomy
TopicsScheduling and Optimization Algorithms