  In constructing an econometric or statistical model, we pick relevant
features or variables from many candidates. A coalitional game is set up to
study the selection problem where the players are the candidates and the payoff
function is a performance measurement in all possible modeling scenarios. Thus,
in theory, an irrelevant feature is equivalent to a dummy player in the game,
which contributes nothing to all modeling situations. The hypothesis test of
zero mean contribution is the rule to decide a feature is irrelevant or not. In
our mechanism design, the end goal perfectly matches the expected model
performance with the expected sum of individual marginal effects. Within a
class of noninformative likelihood among all modeling opportunities, the
matching equation results in a specific valuation for each feature. After
estimating the valuation and its standard deviation, we drop any candidate
feature if its valuation is not significantly different from zero. In the
simulation studies, our new approach significantly outperforms several popular
methods used in practice, and its accuracy is robust to the choice of the
payoff function.
