This paper studies identification for a broad class of
empirical games in a general functional setting.
Global identification results are known for some
specific models, e.g., in some standard auction
models. We use functional formulations to obtain
general criteria for local identification. These
criteria can be applied to both parametric and
nonparametric models, and also to models with
asymmetry among players and affiliated private
information. A benchmark model is developed where
the structural parameters of interest are the
distribution of private information and an
additional dissociated parameter, such as a
parameter of risk aversion. Criteria are derived for
some standard auction models, games with exogenous
variables, games with randomized strategies, such as
mixed strategies, and games with strategic functions
that cannot be derived analytically.