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arXiv · 1812.01955

Computing Bayes-Nash Equilibria in Combinatorial Auctions with Verification

Vitor Bosshard·Benedikt Bünz·Benjamin Lubin·Sven Seuken
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Abstract

We present a new algorithm for computing pure-strategy $\varepsilon$-Bayes-Nash equilibria ($\varepsilon$-BNEs) in combinatorial auctions with continuous value and action spaces. An essential innovation of our algorithm is to separate the algorithm's search phase (for finding the $\varepsilon$-BNE) from the verification phase (for computing the $\varepsilon$). Using this approach, we obtain an algorithm that is both very fast and provides theoretical guarantees on the $\varepsilon$ it finds. Our main technical contribution is a verification method which allows us to upper bound the $\varepsilon$ across the whole continuous value space without making assumptions about the mechanism. Using our algorithm, we can now compute $\varepsilon$-BNEs in multi-minded domains that are significantly more complex than what was previously possible to solve. We release our code under an open-source license to enable researchers to perform algorithmic analyses of auctions, to enable bidders to analyze different strategies, and to facilitate many other applications.

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Vitor Bosshard, Benedikt Bünz, Benjamin Lubin, Sven Seuken. 2018-12-05. Computing Bayes-Nash Equilibria in Combinatorial Auctions with Verification. https://doi.org/10.1613/jair.1.11525

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