Tight Revenue Bounds With Possibilistic Beliefs and Level-k Rationality

• 成果类型: Article
• 署名作者: Chen, Jing; Micali, Silvio; Pass, Rafael
• 署名单位: State University of New York (SUNY) System; Stony Brook University; Massachusetts Institute of Technology (MIT); Cornell University
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA12563
• 发表日期: 2015
• 页码: 1619-1639
• 关键词: VIRTUAL IMPLEMENTATION; mechanism-design; players models; guessing games; BEHAVIOR; hierarchies; strategies; cognition; auctions

摘要

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, center dot 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). center dot 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.