【作者】 谭德庆；

【导师】 胡培；

【作者基本信息】 西南交通大学 ， 管理科学与工程， 2004， 博士

【摘要】 博弈论是研究决策主体的行为发生直接相互作用时的决策以及这种决策的均衡问题。在博弈中，每个参与人的效用函数不仅依赖于他自己选择的策略，而且依赖于其他参与人选择的策略，因此，博弈论研究的是在存在相互外部经济条件下的个人选择问题。博弈论可以划分为合作博弈(cooperative game)和非合作博弈(non-cooperative game)，现在经济学家谈到的博弈论一般指的是非合作博弈。在社会实践和生活中，人们决策行为之间的相互影响的例子很多，比如寡头市场上，企业的价格竞争或者产量竞争；还有国家之间在军事上或经济上的竞争；两个企业在广告上的竞争，等等问题。因此，博弈论的应用在现实中是非常广泛的。 博弈论经过了几十年的迅速发展，无论在理论研究还是在应用研究上都取得了巨大成果。但是在博弈论的应用研究方面所涉及的问题大多是关于两个(或多个)参与人在一个领域或在一个方面的博弈问题，如两个(或多个)寡头关于一种产品的价格或产量的博弈问题、两个(或多个)国家在军事领域内竞争和对抗问题、两个(或多个)国家之间在某一经济领域内的贸易谈判等等博弈问题。从博弈论的广义角度，目前在博弈应用方面的研究成果大多是关于“一维”的博弈问题，即对博弈参与人在一个领域内的博弈问题。然而在现实社会中，普遍存在着更为广泛的另一类博弈，如中国加入WTO谈判，WTO谈判实质是“同时”在多个领域内谈判，并且所谈判的领域之间存在着相互作用或联系；两个(或多个)国家“同时”在经济、科技、军事等多个领域内进行竞争和对抗，并且所竞争的领域之间存在着相互作用或联系；又如在经济活动中，两个(或多个)企业“同时”进行多种产品的价格或产量博弈，并且这些产品之间在市场中存在着相互影响(例如：替代性)；等等。本文把参与人同时在相互具有影响关系的多领域内博弈称为多维博弈。西南交通大学博士研究生学位论文第11页 目前，在应用研究方面对这类多维博弈问题的研究很少，本文主要对经济博弈中的这类连续型多维博弈为重点研究对象，原因是对于连续型多维博弈，通过建模研究能比较充分地体现所博弈的各领域内的机理和相互影响。本文首先研究了完全信息静态多维博弈和完全信息动态多维博弈类型。在这两种类型中，主要探讨了税务机关与企业集团之间的静态多维博弈问题，双寡头Coumot静态二维博弈模型，双寡头Bertrand静态二维博弈模型，两国静态三维博弈模型，产品广告、产品服务投入和价格选择的静态三维博弈模型，双寡头Coumot动态二维博弈模型，产品广告、产品服务投入和价格选择的动态三维博弈模型。其次，研究了不完全信息静态多维博弈和不完全信息动态多维博弈两种类型。在这两种类型中，主要探讨了Bertrand静态二维博弈模型，关于产量策略的静态二维博弈模型，Cournot动态二维博弈模型。最后，研究了企业在对具有一定替代关系的两种产品价格博弈中，企业掌握的信息量对其最优策略向量选择的影响;又探讨了不确定环境下在企业之间多种产品价格的博弈中，参与人考虑收益和风险两个目标如何选择其最优策略向量。 随着经济全球化和中国加入WTO后，国与国之间在多领域内的竞争和对抗也更加普遍和激烈，同时也将有更多跨国公司进入中国，这些必将使市场竞争更加复杂化和更加激烈化，因此有必要对更为复杂和广泛存在的这类多维博弈进行探讨和研究。同时由于这类多维博弈在社会实践和生活中更具广泛性和应用性，因此对其进行研究就更具有重要性和意义。关键词多维博弈总支付静态动态信息均衡更多还原

【Abstract】 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.更多还原