Strategic commitment in a mixed oligopoly

A dynamic three-stage game is modelled to analyse the capacity choice in a mixed oligopoly with private leaders and a public follower. To distinguish long-term and short-term market power, I consider two stages of investment, the first by a private firm and the second by a public one, and one stage of production. Even if firms have the same technology, the short-term market power of the private firm could prevent the public firm from restoring the long-term optimum. Contrary to usual results on commitment, it is the inability of the private firm to commit to a given production level that allows it to get strictly positive profits. This paper establishes that, for low demand elasticity and small share of sunk cost, the private firm is able to get strictly positive profits. This result is no longer true if the order of moves is modified. Furthermore, the effect of the share of sunk cost on the private firm's profit is not monotonic. When the share of sunk cost increases, the commitment value of sunk investment explains that private profit increases in some cases, but, in other cases the effect of short-term market power implies that its profit decreases.