  We study testable implications of multiple equilibria in discrete games with
incomplete information. Unlike de Paula and Tang (2012), we allow the players'
private signals to be correlated. In static games, we leverage independence of
private types across games whose equilibrium selection is correlated. In
dynamic games with serially correlated discrete unobserved heterogeneity, our
testable implication builds on the fact that the distribution of a sequence of
choices and states are mixtures over equilibria and unobserved heterogeneity.
The number of mixture components is a known function of the length of the
sequence as well as the cardinality of equilibria and unobserved heterogeneity
support. In both static and dynamic cases, these testable implications are
implementable using existing statistical tools.
