We investigate tax/subsidy competition for foreign direct investments (FDI) between countries of different size when a domestic firm is the incumbent in the largest market and we study how the nature (public or private) of the incumbent firm affects policy competition. We show that, differently from the case of a private firm, the country hosting the incumbent always benefits from FDI if the domestic firm is a public welfare‐maximizing firm. We also show that the public firm acts as a disciplinary device for the foreign multinational that will always choose the efficient welfare‐maximizing location. An efficiency‐enhancing role of policy competition may then arise only when the domestic incumbent is a private firm, whereas tax competition is always wasteful in the presence of a public firm.