论文标题
具有累积前景理论玩家的游戏的黑盒策略和平衡
Black-Box Strategies and Equilibrium for Games with Cumulative Prospect Theoretic Players
论文作者
论文摘要
偏好关系的中间特性指出，两个彩票的概率混合物应在偏好之间存在。这是独立性的弱化形式，因此在预期效用理论（EUT）中满足。实验性违反中学的行为是有据可查的，几种偏好理论，尤其是累积的前景理论（CPT），不满足于中间。我们证明，只有当它们符合EUT偏好时，CPT的偏好才能满足与之相处。在游戏理论中，玩家的偏好关系缺乏伴侣使得区分玩家的混合动作的两种解释 - 玩家有意识的随机化以及对手信仰的不确定性。我们详细介绍了这种区别，并研究了其对NASH平衡的定义的影响。这导致了四个不同的平衡概念，纯和混合动作nash平衡是其中两个。我们分别将另外两个纯黑框策略纳什均衡配音。我们解决了这种平衡的存在问题，并研究了这些不同的平衡概念如何相互比较。
The betweenness property of preference relations states that a probability mixture of two lotteries should lie between them in preference. It is a weakened form of the independence property and hence satisfied in expected utility theory (EUT). Experimental violations of betweenness are well-documented and several preference theories, notably cumulative prospect theory (CPT), do not satisfy betweenness. We prove that CPT preferences satisfy betweenness if and only if they conform with EUT preferences. In game theory, lack of betweenness in the players' preference relations makes it essential to distinguish between the two interpretations of a mixed action by a player - conscious randomizations by the player and the uncertainty in the beliefs of the opponents. We elaborate on this distinction and study its implication for the definition of Nash equilibrium. This results in four different notions of equilibrium, with pure and mixed action Nash equilibrium being two of them. We dub the other two pure and mixed black-box strategy Nash equilibrium respectively. We resolve the issue of existence of such equilibria and examine how these different notions of equilibrium compare with each other.
