  To what extent can an external observer observing an equilibrium action
distribution in an incomplete information game infer the underlying information
structure? We investigate this issue in a general linear-quadratic-Gaussian
framework. A simple class of canonical information structures is offered and
proves rich enough to rationalize any possible equilibrium action distribution
that can arise under an arbitrary information structure. We show that the class
is parsimonious in the sense that the relevant parameters can be uniquely
pinned down by an observed equilibrium outcome, up to some qualifications. Our
result implies, for example, that the accuracy of each agent's signal about the
state is identified, as measured by how much observing the signal reduces the
state variance. Moreover, we show that a canonical information structure
characterizes the lower bound on the amount by which each agent's signal can
reduce the state variance, across all observationally equivalent information
structures. The lower bound is tight, for example, when the actual information
structure is uni-dimensional, or when there are no strategic interactions among
agents, but in general, there is a gap since agents' strategic motives confound
their private information about fundamental and strategic uncertainty.
