Tight Revenue Bounds With Possibilistic Beliefs and Level‐ k Rationality

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, G 0 ≤ G 1 ≤ G 2 ≤⋯, where each G i is defined over the players' beliefs and G 0 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 G k if all players have rationality levels ≥ k +1, and (2) prove that no such mechanism can guarantee revenue even close to G k when at least two players are at most level‐ k rational.