摘要
本文研究含有模糊不对称信息情况下的决策问题.分别从模糊不完全信息下的决策问题、模糊不对称信息产生的原因、决策人根据观测更新主观判断的方法、模糊不对称信息的对策问题以及模糊不对称信息委托代理问题这五个方面展开论述.
首先提出模糊映射来描述决策环境中目标受若干模糊参数的影响.得出当模糊参数满足相互独立以及模糊映射对应函数满足单调性时,模糊映射的期望值函数能保持原函数的连续性和凸性,为定性以及定量地分析并作出合理决策提供理论分析依据.
分析了模糊不对称信息产生的原因,从非共同信息的角度出发,给出了两种定义近似共同信息的方法:近似交替共同信息和近似互知共同信息,并分析了各自的性质及两者之间的关系.得出非共同信息可在一定可信性水平下构成近似共同信息.
根据决策人在决策过程中会不断收集信息以更新对环境的主观判断之特点,提出一种模糊参数统计推断方法-模糊点估计法.特别是当样本规模较小的时候,所设计之统计推断方法可有效地用来更新决策者对模糊环境的主观判断.
针对现实生活中诸多博弈问题既含有随机性又含有模糊性,以及信息的不对称性等特点,建立了有限模糊类型的静态贝叶斯博弈模型,同时结合可信性理论建立了参与人的决策准则,在此基础上分析并证明了均衡的存在性.建立了模糊不对称信息委托代理模型.将委托人关于代理人类型的主观不确定性刻画成模糊变量,把契约设计成二维变量:一个行动变量和一个转移支付变量.分别给出了最优契约的充分性和必要性条件.进一步地,考虑了行动变量和转移支付变量满足一阶导函数有界情况下的最优契约.
分别通过研究模糊环境下零售商最优订货决策问题、不对称信息下具有模糊效率的古诺竞争问题及模糊不对称信息情况下供应链管理中的契约设计问题,验证了所给出的理论模型和处理方法的有效性.
This dissertation studies decision-making problems with fuzzy asymmetricinformation, and it can be divided into five parts: a single-person decision-makingproblem with imprecise information; the nature of the fuzzy asymmetric informa-tion; fuzzy parametric statistical inference method; multi-person decision makingproblem; and fuzzy principal-agent problem.
From the perspective of a single-person decision-making problem, the con-cept of fuzzy mapping is proposed to describe the decision problem, where thetarget is a?ected by several fuzzy parameters. It proves that the continuity andconvexity can be inherited after calculating the expected value on the hypothesesof monotonicity of the corresponding function and the upper semi-continuous ofthe membership functions of independent fuzzy variables. This method providesa theoretical approach to analyze such problem qualitatively as well as quantita-tively, and helps to make decisions rationally.
The nature of the fuzzy asymmetric information is studied next. As onekind of non-common knowledge, this dissertation considers how a fuzzy eventcan be analyzed as an approximate common knowledge with some credibility,which is defined iteratively and mutually, iteratively and mutually knows withsome credibility.
Fuzzy parametric statistical inference method is developed to renew thejudgment about the fuzzy parameters. This method can be applied by the deci-sion maker to update his subjective beliefs of the fuzzy environment, especiallywhen there is only a small sample available.
For the multi-person decision making problem, this dissertation studies aspecial game with incomplete information, in which the payo?s of the players areboth random and fuzzy. A static fuzzy Bayesian game is then introduced andthe decision rules for players are given based on credibility theory. We furtherprove the existence of the equilibrium of the game.
For the principal-agent problem, where the agent has some private informa-tion which is characterized as a fuzzy variable by the principal, a fuzzy principal-agent model is proposed in this dissertation. In the model, a contract variable isdevised with two dimensions: an action variable and a transfer variable. The suf-ficient conditions and necessary conditions for the optimal contract are explored.Furthermore, we provide an optimal contract for a special case, where the actionvariable and the transfer variable have finite first-order derivatives.
Three practical problems, i.e., retailer’s optimization problem under fuzzyenvironments, Cournot competition with fuzzy e?ciency and the optimal con-tract design in supply chain management under fuzzy environments are discussedseparately to verify the e?ectiveness of the models and methods developed in thisdissertation.
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