基于风险厌恶者的连续对策之随机占优均衡  

Stochastic Dominance Equilibria for Risk Averse Players in a Continuous Game

作　　者：熊国强[1] 

机构地区：[1]西安理工大学工商管理学院,陕西西安710054

出　　处：《系统工程》2007年第8期79-83,共5页Systems Engineering

基　　金：国家自然科学基金资助项目(70272063)

摘　　要：一般对策理论中只把局中人为风险厌恶者作为一种隐性假定,没有给出明确的判别特征,本文在对局中人的风险厌恶态度划分阶次的基础上,引入连续对策上的t阶风险厌恶者、随机占优下的t阶最优策略和t阶均衡解等概念,研究了t阶均衡解与经典Nash均衡之间的关系,以及t阶均衡解存在的充分必要条件。得到了如下几个主要结果:(1)可用支付函数的高阶导数的符号判别任意阶次的风险厌恶者,阶次的大小对应对策参与人风险厌恶的不同程度;(2)t阶均衡解集等价于其Nash均衡解集;(3)直接用分布函数的阶次特征来识别t阶最优策略和t阶均衡解。Players are risk averseness was regarded as a recessive hypothesis in general game theory, which didn＇t offer any specific distinguishing character. This paper introduces such definitions as t-degree risk averse of a continuous game, t-optimal strategies of stochastic dominance and t-equilibrium etc. , researches the relationship between t-equilibrium and classical Nash equilibrium and sufficient and necessary conditions of t-equilibrium being, which are based on dividing the risk averse attitudes of players into different degree. We obtain the following results.. （1） Risk averse player with any degree can be judged by higher-order derivative＇s sign of payoff function, different degrees are corresponding to different risk averse degrees of game participants; （2） The set of t-equilibrium is equal to the set of its Nash equilibrium; （3） The t-optimal strategies and t-equilibrium can be directly distinguished by t-degree character of probability distribution function.

关 键 词：连续对策 随机占优 t阶最优策略 t阶均衡解 

分 类 号：O225[理学—运筹学与控制论]