Price of Anarchy for Greedy Auctions
Brendan Lucier (1), Allan Borodin (1) ((1) University of Toronto)
TL;DR
This paper analyzes the efficiency loss in auctions that use greedy algorithms for allocation, showing that the worst-case social welfare ratio at equilibrium closely matches the greedy algorithm's approximation ratio.
Contribution
It establishes bounds on the price of anarchy for greedy auctions with various equilibrium concepts, linking it to the algorithm's approximation factor.
Findings
Price of anarchy bounds are close to the greedy algorithm's approximation ratio.
Results hold for multiple equilibrium concepts including Bayes-Nash and correlated equilibrium.
Provides theoretical guarantees on auction efficiency loss in multi-parameter settings.
Abstract
We consider auctions in which greedy algorithms, paired with first-price or critical-price payment rules, are used to resolve multi-parameter combinatorial allocation problems. We study the price of anarchy for social welfare in such auctions. We show for a variety of equilibrium concepts, including Bayes-Nash equilibrium and correlated equilibrium, the resulting price of anarchy bound is close to the approximation factor of the underlying greedy algorithm.
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Taxonomy
TopicsAuction Theory and Applications · Economic theories and models · Game Theory and Voting Systems