Uncertainty in Mechanism Design

Abstract

This paper studies the design of mechanisms that are robust to misspecification. We introduce a novel notion of robustness that connects a variety of disparate approaches and study its implications in a wide class of mechanism design problems. This notion is quantifiable, allowing us to formalize and answer comparative statics questions relating the nature and degree of misspecification to sharp predictions regarding features of feasible mechanisms. This notion also has a behavioral foundation which reflects the perception of ambiguity, thus allowing the degree of misspecification to emerge endogenously. In a number of standard settings, robustness to arbitrarily small amounts of misspecification generates a discontinuity in the set of feasible mechanisms and uniquely selects simple, ex post incentive compatible mechanisms such as second-price auctions. Robustness also sheds light on the value of private information and the prevalence of full or virtual surplus extraction.

Maxmin implementation

“…In contrast, we consider a MD who intentionally creates ambiguity for MEU agents to implement her desired outcomes. Thus, our approach connects to the literature studying ambiguity averse agents, including Bose et al (2006), Bose and Daripab (2009), L.Bodoh-Creed (2012), Bose and Renou (2014), Wolitzky (2016), Song (2018), Lopomo et al (2020), etc. In those papers, agents have ambiguous or misspecified beliefs over others' types or the underlying states.…”

Ambiguous persuasion

“…6 This phenomenon has attracted significant interest in theory and applications. 7 The literature that explores the role of ambiguity aversion in games and mechanisms has been steadily growing (Ayouni and Koessler, 2017;Bose et al, 2006;Di Tillio et al, 2016;Frankel, 2014;Lopomo et al, 2011Lopomo et al, , 2014Wolitzky, 2016). Bade (2011) and Riedel and Sass (2014) both study complete information games where the players, in addition to playing mixed strategies, are allowed to use ambiguous strategies in a manner similar to ours.…”

Continuous level-k mechanism design

“…See also McLean and Postlewaite (2002) and Weinstein and Yildiz (2007) for related robustness concerns beyond implementation. For other approaches that model versions of global (as opposed to local) robustness, in the sense that the model is tested against a wide class of mispecifications, see, e.g., Morris (2005, 2012), Artemov et al (2013), Ollár and Penta (2017), and Lopomo et al (2020).…”