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...and that the public firm chooses not be a leader of all foreign private firms, which is in contrast to Matsumura (2003).
Keywords: mixed oligopoly, endogenous timing, foreign competitors.
JEL Classification: L13, D43, H42.
1 Introduction
Studies of mixed markets, in which welfare-maximizing public firms compete against profit-maximizing private firms, have become increasingly popular in recent years. (1) The mixed oligopoly consists of public firms and domestic private firms in most of the literature on mixed oligopoly, but foreign private firms are also included in a few studies. For example, Corneo and Jeanne (1994) considered mixed oligopolies in an international setting where public firms compete with domestic private firms and foreign private firms, characterized the equilibrium and explored welfare implications of nationalization, privatization and the creation of a public firm. Fjell and Pal (1996) investigated the effect of the introduction of foreign private firms on the equilibrium price and allocation of production (relative to the case when all private firms are domestically owned); Fjell and Heywood (2002) considered a mixed oligopoly in which a public Stackelberg leader competes with both domestic and foreign private firms.
In the literature on mixed oligopoly, most of the articles assume firms make quantity choices simultaneously or sequentially and the order of moves is treated as exogenously given. There also have been some papers discussing endogenous timing in a mixed oligopoly since an alternate order of moves often produces significantly different results and thus leads to different welfare level. For example, Pal (1998) analyzed endogenous order of moves in quantity choice in a mixed oligopoly consisting of a single public firm and n domestic private firms. (2) Matsumura (2003) considered endogenous roles of firms in a mixed duopoly market where a state-owned public firm and a foreign private firm compete.
However, there is no paper discussing endogenous timing in a mixed oligopoly with both domestic and foreign private firms. There are no foreign private firms in Pal (1998) and no domestic private firms in Matsumura (2003). In reality, public firms, domestic private firms and foreign private firms coexist in many industries and in many countries. The electricity industry in some european countries such as Germany and France is a good example after the deregulation of electricity in the European Union. (3) So the endogenous timing in such a mixed oligopoly is very important and it is surprising that there is no paper discussing such a question. The purpose of this paper is to fill in this gap and to address the issue of endogenous timing in a mixed oligopoly consisting of a public firm, domestic and foreign private firms, in particular, to investigate the impact of the introduction of foreign private firms on the endogenous timing in a mixed oligopoly.
Hamilton and Slutsky (1990) is a seminal work in the endogenous timing literature. In this paper, the authors considered two different extended games in the context of a quantity setting duopoly: one is the extended game with observable delay and the other is the extended game with action commitment. In this paper, we consider the extended game with observable delay in the context of a quantity setting mixed oligopoly where firms first announce in which period they will choose their quantities and are committed to this choice before they actually choose their quantities and the mixed oligopoly consists of one public firm, n([greater than or equal to] 1) domestic private firms and m([greater than or equal to] 1) foreign private firms. At this stage, we focus on the linear demand case. We find that in any equilibrium, the public firm chooses to be a follower of all domestic private firms, the public firm chooses not to be a leader of all foreign private firms, which is in contrast to Matsumura (2003), and that the number of subgame perfect Nash equilibria (SPNE) depends on the number of the domestic private firms and that of the foreign private firms.
The organization of the paper is as follows. In Sect. 2, we describe the model. Section 3 presents the results when there are only three possible periods for quantity choice. The SPNEs are presented in Sect. 4 when there are more than three possible periods to be chosen. Section 5 concludes the paper.
2 The Model
Consider a mixed oligopoly model with one public firm, n([greater than or equal to] 1) domestic private firms and m([greater than or equal to] 1) foreign private firms, all producing a single homogenous product. Let [q.sub.0], [q.sub.i.sup.d] and [q.sub.j.sup.f] be the quantities of the public firm, of domestic private firm i and of foreign private firm j, respectively. Let Q = [q.sub.0] + [[summation].sub.i=1.sup.n][q.sub.i.sup.d] + [[summation].sub.j=1.sup.m] [q.sub.j.sup.f] denote the aggregate quantity. The market price is determined by the inverse demand function p = a - Q. Assume that a is sufficiently large. All domestic and foreign private firms have constant and identical marginal costs of production, which are normalized to 0. (4)
The public firm also has constant marginal cost of production. To make the results in this paper directly comparable to those of Pal (1998), the public firm is assumed to be less efficient than the private firms. (5) Let c > be the marginal cost of the public firm. For the sake of simplification, fixed costs are assumed to be zero for all firms.
We consider the observable delay game of Hamilton and Slutsky (1990) in the context of a quantity setting mixed oligopoly where firms first announce at which time they will choose their quantities and are committed to this choice before they actually choose their quantities. There are T [greater than or equal to] 3 possible periods for quantity choice and each firm may choose its quantity in only one of those T periods. We consider a two stage game. In stage one, the firms simultaneously announce in which period they will choose their quantities and are committed to this choice. In stage two, after the announcement, firms then choose their quantities knowing when the other firms will make their quantity choices.
The public firm's objective is to maximize domestic social surplus defined as the sum of consumer surplus and profits of domestic firms (including itself and all domestic private firms), whereas each private firm's objective is to maximize its own profit. Thus, the objective functions of the public firm, of domestic private firm i and of foreign private firm j are...
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