Tight revenue bounds with possibilistic beliefs and level-k rationality
Name
Chen, Micali, Pass (2015) Tight revenue bounds.pdf
Description
Final published version.
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582.74 KB
Format
Adobe PDF
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Author(s)
Chen, Jing
Micali, Silvio
Pass, Rafael
Date Issued
July 2015
Publisher
© The Econometric Society
Citation
Chen, J., Micali, S., & Pass, R. (2015). Tight revenue bounds with possibilistic beliefs and level-k rationality. Econometrica, 83(4), 1619–1639.
Version
Final published version.
Abstract
Mechanism design enables a social planner to obtain a desired outcome by leveraging the players’ rationality and their beliefs. It is thus a fundamental, but yet unproven, intuition that the higher the level of rationality of the players, the better the set of obtainable outcomes.
In this paper, we prove this fundamental intuition for players with possibilistic beliefs, a model long considered in epistemic game theory. Specifically,
• We define a sequence of monotonically increasing revenue benchmarks for single- good auctions, G0 ≤ G1 ≤ G2 ≤ · · ·, where each Gi is defined over the players’ beliefs and G0 is the second-highest valuation (i.e., the revenue benchmark achieved by the second-price mechanism).
• We (1) construct a single, interim individually rational, auction mechanism that, without any clue about the rationality level of the players, guarantees revenue Gk if all players have rationality levels ≥ k + 1, and (2) prove that no such mechanism can guarantee revenue even close to Gk when at least two players are at most level-k rational.
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