Verifying Approximate Equilibrium in Auctions
Fabian R. Pieroth, Tuomas Sandholm

TL;DR
This paper introduces a novel, sample-based framework for verifying approximate equilibria in complex auctions, accounting for strategic bidding and interdependent priors, with theoretical error bounds and broad applicability.
Contribution
It presents the first method to verify approximate equilibrium in diverse auction types using samples, considering strategic and interdependent priors, with PAC-learning error bounds.
Findings
Developed a framework for estimating utility gains from strategic deviations.
Provided error bounds for approximate equilibrium verification using PAC-learning.
First method to verify approximate equilibrium in various auction formats beyond single-item.
Abstract
In practice, most auction mechanisms are not strategy-proof, so equilibrium analysis is required to predict bidding behavior. In many auctions, though, an exact equilibrium is not known and one would like to understand whether -- manually or computationally generated -- bidding strategies constitute an approximate equilibrium. We develop a framework and methods for estimating the distance of a strategy profile from equilibrium, based on samples from the prior and either bidding strategies or sample bids. We estimate an agent's utility gain from deviating to strategies from a constructed finite subset of the strategy space. We use PAC-learning to give error bounds, both for independent and interdependent prior distributions. The primary challenge is that one may miss large utility gains by considering only a finite subset of the strategy space. Our work differs from prior research in two…
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Taxonomy
TopicsAuction Theory and Applications · Economic theories and models · Merger and Competition Analysis
