This paper develops and estimates a game-theoretical model of inflation targeting where the central banker's preferences are asymmetric around the targeted rate. Specifically, positive deviations from the target can be weighted more, or less, severely than negative ones in the central banker's loss function. It is shown that some of the previous results derived under the assumption of symmetry are not robust to this generalization of preferences. Estimates of the central banker's preference parameters for Canada, Sweden, and the United Kingdom are statistically different from the one implied by the commonly-used quadratic loss function.