Endogenous timing in a mixed duopoly
Two firms, a private profit maximizing one and a public social welfare maximizing one, compete in quantities and their products are homogeneous. Using games to such a mixed quantity duopoly market a main question is to decide which kind of games and equilibria should be considered, here: simultaneous (Cournot) or sequential (Stackelberg) game. The authors show, that this decision and also, who is leader or follower in the Stackelberg case, can be determined endogenously adding a preplay to the duopoly game in the sense as in [\textit{J. H. Hamilton} and \textit{S. M. Slutsky}, Games Econ. Behav. 2, No. 1, 29--46 (1990; Zbl 0753.90074)]. Then, under certain assumptions, it is proved, that the wanted decision is Stackelberg game, and -- as the authors write -- the most plausible outcome is public leadership, when the private firm is foreign, and public or private leadership, when the private firm is domestic. The conclusion of the paper also gives a lot of hints from the economic point of view, e.g. on the effect of privatization. From the mathematical point of view the stated assumptions for this part of game theory are interesting: only pure strategies are dealt with, the inverse demand function has esp. to be twice continuously differentiable, the cost functions also and they must be increasing, sometimes (f.i. in Theorem 5) convex, an interiority assumption on simultaneously-move equilibria must hold. A big appendix contains proofs using the mentioned assumptions and the smooth implicit function theorem, the envelope theorem and Dini derivatives together with results of the theory of supermodular games.
scientific article; zbMATH DE number 6336297