在存在累计前景博弈者的博弈论下的黑盒策略与平衡(cs.GT)---用户7199428

偏好关系的中间属性规定了两个彩票的可能性混合应该在这两个彩票的偏好之间。它是独立属性的一种弱化形式，并且因此满足于期望效应理论（EUT）。实验中对于中间属性的违背都被很好地记录下来，并且一些偏好理论，尤其是累积前景理论（CPT），并不能很好地满足中间性。我们证实到的是，只有当CPT偏好满足EUT偏好时，才能符合中间性。在博弈论中，一旦缺少博弈者偏好关系的中间属性，就使区分两种解释，一个是博弈者意识下的随机混合行为，另一个是对于对手意图下的不确定性，变得至关重要。我们详细阐述了区分方式和其在纳什平衡下的潜在含义。结果中有4个不同的平衡概念，其中两个是完全和混合的纳什平衡操作。我们则给另外两个分别起别名为黑盒版的完全和混合的纳什平衡。我们解决了这种平衡的存在问题并且仔细审查了这些不同概念的平衡是如何互相比较的。

原文题目：Black-Box Strategies and Equilibrium for Games with Cumulative Prospect Theoretic Players

原文：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.

原文作者：Soham R. Phade, Venkat Anantharam

原文地址：https://arxiv.org/abs/2004.09592