A market competition game with sequential pricings

In an oligopoly market we consider a pricing game by a leader firm and follower firms. After the leader firm determines the price of his goods, the other firms determine the prices of their goods knowing not the prices of other followers' goods but the price of the leader's goods. It is assumed that the market share of each firm changes under the effect of price differences. This market model is formulated by a n -person nonzero-sum two-stage game with complete but imperfect information and its subgame-perfect Nash equilibrium is obtained. Next we analyze a pricing problem in the entry of a new firm into a monopoly market. Furthermore in a duopoly market we discuss the motive for a firm to change his price and obtain the stationary state (the stable equilibrium point) which both players attain ultimately by sequential pricings.