  We study the problem of characterizing the set of games that are consistent
with observed equilibrium play. Our contribution is to develop and analyze a
new methodology based on convex optimization to address this problem for many
classes of games and observation models of interest. Our approach provides a
sharp, computationally efficient characterization of the extent to which a
particular set of observations constrains the space of games that could have
generated them. This allows us to solve a number of variants of this problem as
well as to quantify the power of games from particular classes (e.g., zero-sum,
potential, linearly parameterized) to explain player behavior. We illustrate
our approach with numerical simulations.
