In the last mixed bill of New York City Ballet’s winter season, “Contemporary Choreography II,” the company’s resident choreographer Alexei Ratmansky premieres The Naked King, after Hans Christian Andersen’s short story “The Emperor’s New Clothes.” The one-act ballet is a sardonic nod to our own de facto king as well as his sycophantic flunkies. Ratmansky possesses a brilliant knack for the comedy of dumb power. For this outing, he has Jean Françaix’s witty 1935 score for the Paris Opera Ballet to help. Christopher Wheeldon’s lush pas de deux This Bitter Earth and two Justin Pecks (the recent amuse-bouche Dig the Say and the sweetly comradely Everywhere We Go) complete the program. —Apollinaire Scherr