On the Relationship between Robustness to Incomplete Information and Noise-Independent Selection in Global Games

This note demonstrates that a symmetric 3x3 supermodular game may fail to have any equilibrium robust to incomplete information. Since the global game solution in symmetric 3x3 supermodular games is known to be independent of the noise structure, this result implies that a noise-independent selection in global games may not be a robust equilibrium. Our proof reveals that the assumption in global games that the noise errors are independent of the state imposes a non-trivial restriction on incomplete information perturbations