Imperfect Public Monitoring with a Fear of Signal Distortion

52 Pages Posted: 7 Nov 2014 Last revised: 22 Apr 2017

See all articles by Vivek Bhattacharya

Vivek Bhattacharya

Northwestern University

Lucas Manuelli

Massachusetts Institute of Technology (MIT) - Department of Economics

Ludwig Straub

Massachusetts Institute of Technology (MIT), Department of Economics, Students

Date Written: March 24, 2017

Abstract

This paper proposes a model of signal distortion in a two-player game with imperfect public monitoring. We construct a tractable theoretical framework where each player has the opportunity to distort the true public signal and each player is uncertain about the distortion technologies available to the other player. We show that when players evaluate strategies according to their worst-case guarantees—i.e., are ambiguity averse over certain distributions in the environment—perceived continuation payoffs endogenously lie on a positively sloped line. We then provide examples showing that, counterintuitively, identifying deviators can be harmful in enforcing a strategy profile; moreover, we illustrate how the presence of such signal distortion can sustain cooperation when it is impossible in standard settings. We show that the main result and examples are robust to a number of natural modifications to our setting. Finally, we extend our model to a repeated game where our concept is a natural generalization of strongly symmetric equilibria. In this setting, we prove an anti-folk theorem, showing that payoffs under our equilibrium concept are under general conditions bounded away from efficiency.

Keywords: linearity, imperfect public monitoring, repeated games, ambiguity aversion

JEL Classification: C72, C73, D83

Suggested Citation

Bhattacharya, Vivek and Manuelli, Lucas and Straub, Ludwig, Imperfect Public Monitoring with a Fear of Signal Distortion (March 24, 2017). MIT Department of Economics Graduate Student Research Paper No. 14-02. Available at SSRN: https://ssrn.com/abstract=2519260 or http://dx.doi.org/10.2139/ssrn.2519260

Vivek Bhattacharya (Contact Author)

Northwestern University ( email )

Lucas Manuelli

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

Ludwig Straub

Massachusetts Institute of Technology (MIT), Department of Economics, Students ( email )

Cambridge, MA
United States

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