论文标题
比较零和游戏的信息结构，与标准鲍勒空间中的Blackwell订购的部分交谈
Comparison of Information Structures for Zero-Sum Games and a Partial Converse to Blackwell Ordering in Standard Borel Spaces
论文作者
论文摘要
在涉及单个决策者的统计决策理论中，如果涉及隐藏状态变量的任何成本函数和一个限制在有条件地独立于状态的，则信息结构比另一个更好，而前者下的解决方案值并不比后者差。对于有限的空间，由于Blackwell引起的定理会导致一个信息结构何时比另一个信息更好。对于随机游戏来说，通常不可能进行这种订购，因为其他信息可能会导致竞争者的平衡扰动或负值。但是，对于有限概率空间中的零和游戏，PęSki引入了信息结构的订购的完整表征。在本文中，我们获得了PęSKI结果的无限维度（标准Borel）概括。推论是，更多的信息不会损害参加零和游戏的决策者。我们建立了两个支持结果，这些结果是必不可少的，尽管对先前的文献进行了适度的改进：（i）与布莱克韦尔在标准Borel设置中的订购的部分交谈，以及（ii）在零和游戏中具有不完整信息的零和游戏中平衡的结果。
In statistical decision theory involving a single decision-maker, an information structure is said to be better than another one if for any cost function involving a hidden state variable and an action variable which is restricted to be conditionally independent from the state given some measurement, the solution value under the former is not worse than that under the latter. For finite spaces, a theorem due to Blackwell leads to a complete characterization on when one information structure is better than another. For stochastic games, in general, such an ordering is not possible since additional information can lead to equilibria perturbations with positive or negative values to a player. However, for zero-sum games in a finite probability space, Pęski introduced a complete characterization of ordering of information structures. In this paper, we obtain an infinite dimensional (standard Borel) generalization of Pęski's result. A corollary is that more information cannot hurt a decision maker taking part in a zero-sum game. We establish two supporting results which are essential and explicit though modest improvements on prior literature: (i) a partial converse to Blackwell's ordering in the standard Borel setup and (ii) an existence result for equilibria in zero-sum games with incomplete information.
