Tight Revenue Bounds With Possibilistic Beliefs and Level-kRationality

Econometrica · 2015 · Volume 83 · Issue 4

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 thatthe 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 withpossibilistic beliefs, a model long considered in epistemic game theory. Specifically, • We define a sequence ofmonotonically increasingrevenue benchmarks for single-good auctions,G0≤G1≤G2≤⋯, where eachGiis defined over the players' beliefs andG0is 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 clueabout the rationality level of the players, guarantees revenueGkif all players have rationality levels ≥k+1, and (2) prove that no such mechanism can guarantee revenue even close toGkwhen at least two players are at most level-krational.

Keywords

Epistemic game theory, incomplete information, single-good auctions

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