Subgame-perfect Implementation under Information Perturbations*

We consider the robustness of extensive form mechanisms to deviations from common knowledge about the state of nature, which we refer to as information perturbations. First, we show that even under arbitrarily small information perturbations the Moore-Repullo mechanism does not yield (even approximately) truthful revelation and that in addition the mechanism has sequential equilibria with undesirable outcomes. More generally, we prove that any extensive form mechanism is fragile in the sense that if a non-Maskin monotonic social objective can be implemented with this mechanism, then there are arbitrarily small information perturbations under which an undesirable sequential equilibrium also exists. Finally, we argue that outside options can help improve effi ciency in asymmetric information environments, and that these options can be thought of as reflecting ownership of an asset. ∗This paper builds on two preliminary contributions, respectively by Aghion, Fudenberg and Holden (2009) and Kunimoto and Tercieux (2009). †Aghion: Harvard University, Department of Economics and CIFAR; email: [email protected]. Fudenberg: Harvard University, Department of Economics; email: [email protected]. Holden: University of New South Wales, Australian School of Business; email: [email protected] Kunimoto: Department of Economics, Hitotsubashi University, Tokyo, Japan; email [email protected]. Tercieux: Paris School of Economics, Paris, France; email: [email protected]. We thank Oliver Hart, Johannes Horner, John Moore and Andy Skrzypacz for detailed comments on earlier drafts. We are also grateful to Ken Binmore, Yeon-Koo Che, Mathias Dewatripont, Bob Gibbons, Ed Green, Matt Jackson, Philippe Jehiel, Hitoshi Matsushima, Eiichi Miyagawa, Eric Maskin, Roger Myerson, Antonio Penta, Andrew Postlewaite, Jean Tirole, Jorgen Weibull, Ivan Werning, Tom Wilkening, Muhamet Yildiz, seminar participants at Chicago Booth, Harvard, the Paris School of Economics, Stockholm University, the Stockholm School of Economics, Simon Fraser University, Boston University, Bocconi University, the Max Planck Institute in Bonn, and the Canadian Institute for Advanced Research, and the referees and editor of this journal for very useful comments and suggestions. Thanks also to Ashley Cheng for careful proofreading. Financial support from CIFAR (Aghion), from NSF grants SES 0648616, 0954162 (Fudenberg), and from FQRSC, SSHRC of Canada, and the Seimeikai Foundation (Kunimoto) is gratefully acknowledged.