Study On Multidimensional Game And Its Application

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 depends on his own chosen strategy but also depends on other players' 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 are many such examples as product price competition or product output competition or advertisement competition among enterprises in market, competition in military affair or business among countries, and so on. Hence, game theory is very extensively applied.Although game theory have developed for decades, so far, problems 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 oligarchs, only contest in military affair among countries. Those fruits that we have obtained in application, speaking in broad 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 many kinds of product price (or output), in which there are affect on each other (for example, substitutions), 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 paper makes main research into the successive multidimensional game. The main reason is that modeling sufficiencily reflects inner mechanism and relation in game fields. Firstly, the paper researchs static multidimensional game with complete informationand dynamic multidimensional game with complete information that include multidimensional game between tax department and enterprise bloc, static two-dimensional Cournot model, static two-dimensional Bertrand model, static multidimensional game between two countries, static multidimensional game for product advertisement, product service and product price between two firms, dynamic two-dimensional Cournot model, dynamic multidimensional game for product advertisement, product service and product price between two firms. Secondly, the paper researchs static multidimensional game with incomplete information and dynamic multidimensional game with incomplete information that include static two-dimensional Bertrand model, static two-dimensional Cournot model, dynamic two-dimensional Cournot model. Finally, the paper discusses that in multidimensional game, affect of information capacity on players' selection for optimal strategy vector is analyzed, and in uncertain game environments, how to select a optimal strategy vector under criterion of profit and risk.With economy globalized and China joined WTO, competition and countermine in many fields are gradually pricking up among countries, at the same time, more MNC will enter China. Those must complicate market and intensely compete in market. Therefore, it is necessary to research into more complex and generalized multidimensional game.In a word, since multidimensional game is characterized with universality and application in social practice and life, it is more important and significant to study multidimensional game.