We construct a simple game-theoretic model in which one private firm and one public (or state-owned) firm compete in quantity of goods produced or service provided. The private and public firms each decide how many workers with public service motivation they will employ as part of an incentive scheme. We assume that both firms produce homogeneous goods with a quadratic cost function but that the private firm is more efficient than the public firm. Both firms are faced with linear inverse demand. We show that whether public firms employ more workers with public service motivation than private firms depends on the efficiency gap between the public and private sectors. This result explains why some literature in public administration reports a significant difference in public service motivation between employees in the private and public sectors and the other literature does not.