Better Outcomes from More 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, 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, the traditional model of 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 get even close to guarantee revenue Gk when at least two players are at most level-k rational.

Paper by: Jing Chen Silvio Micali Rafael Pass