格值矩阵博弈研究  

Study on Matrix Games with Lattice-valued Payoffs

作　　者：张霖[1] 徐扬[2] 

机构地区：[1]西南交通大学经济管理学院,成都610031 [2]西南交通大学数学学院,成都610031

出　　处：《计算机科学》2014年第9期229-231,242,共4页Computer Science

基　　金：国家自然科学基金(61175055);工业和信息化部无线电管理局项目([2011]146)资助

摘　　要：博弈论被广泛应用于描述和解决复杂的主体行为相互作用的决策问题。目前对于非实数值领域的博弈问题,成果很少,故研究支付值为格值类型的二人零和矩阵博弈。基于该类型博弈的特殊性,定义了纯战略纳什均衡解和准均衡解以及混合战略纳什均衡解和准均衡解,并研究解的性质,给出获得解的方法,得到各种解存在的充分必要条件。最后,给出了实例,验证了该方法处理支付值为格值类型的博弈问题的可行性和有效性。Game theory has been applied widely to interpret and solve the complex and interrelated decision problems. There are few results on non-real valued domain game. This paper investigated two person zero-sum matrix games with lattice-valued payoffs. New equilibrium solutions, i. e. pure strategy Nash equilibrium solution and quasi equilibrium solution,mixed strategy Nash equilibrium solution and quasi equilibrium solution were defined based on the specificity of this kind of game. The properties of equilibrium solutions were studied. The approaches of obtaining equilibrium solutions were proposed. The sufficient and necessary conditions that strategies are the equilibrium solutions were given. Finally, an example was shown to verify the feasibility and effectiveness of the new method dealing with the two person zero-sum matrix games with lattice-valued payoffs.

关 键 词：矩阵博弈 均衡解 格值支付 不确定性支付 

分 类 号：F224[经济管理—国民经济]