The Two Weibochuande Game And Production Capacity Limit

Game theory is about study on decision makers' decision making and its equilibrium when their actions directly interact on each other. In game, each player's utility function not only depend on his own chosen strategy but also depend on other player's chosen strategies. Therefore, game theory is about research on problem of individual choice in the condition of their exterior economy all existing. Game theory includes cooperative game and non-cooperative game, the game theory that economist now talk about generally refers to non-cooperative game. In social practice and life, there arc many such examples as product price competition or product output competition or advertisement competition among firms in market,competition in military affair or business among countries, and so on. Hence, game theory is extensively applied.Although game theory have developed for decades, so far, problem researched in game theory and application are about that two(or many) players participate in game in one field such as game on a kind of product price among oligopoly only contest in military affair among countries. Those fruits that we have obtained in application, speaking in board sense, belong to category of one-dimensional game problems.However, in really social activities, there is more extensively a kind of game, such as two(or many)countries at the same time compete in three fields which are economy, science and technology, military affair, in which there are interactions or relationships, such as in economic activity, two(or many) firms at the same time game for mangy kinds of product price (or output), in which there are affect on each other (for example, substitutions or complements),and so on. The kind of game is called for multidimensional game in the paper.So far, in application research, study on the kind of game is less. The Bertrand duopoly model is extended based on the influence of correlative product in demand in order to accommodate to the research of the problem, which surmounts the defect that the present Bertrand duopoly models do not meet the research of Bertrand game under the influence of correlative duopoly product in demand. Meanwhile, the two firms compete with price as the strategic variable and the firms are limited by capacity constraints. When the lower-priced firm cannot meet market demand...