SIAM Journal on Control and Optimization, Volume 59, Issue 3, Page 1781-1803, January 2021.
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, Peͅski introduced a complete characterization of ordering of information structures. In this paper, we obtain an infinite-dimensional (standard Borel) generalization of Peͅski'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.

中文翻译：

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零和游戏的信息结构比较以及标准Borel空间中与Blackwell排序部分相反的信息结构

SIAM控制与优化杂志，第59卷，第3期，第1781-1803页，2021年1月。
在涉及单个决策者的统计决策理论中，如果对于涉及隐性状态变量和作用变量的任何成本函数而言，信息结构被认为要优于另一种信息结构，而该行为变量被限制为有条件地独立于给定某种量度的状态，前者下的解决方案价值并不比后者下的解决方案价值差。对于有限空间，由布莱克韦尔定理得出的定理可以完全表征一种信息结构何时优于另一种信息结构。通常，对于随机游戏，这种排序是不可能的，因为附加信息会导致对玩家的正负值均衡波动。但是，对于有限概率空间中的零和游戏，Peͅski引入了信息结构顺序的完整表征。在本文中，我们获得Peͅski结果的无穷大（标准Borel）概括。一个必然的结论是，更多信息不会伤害参与零和博弈的决策者。我们建立了两个支持性的结果，尽管对现有文献进行了适度的改进，但这些结果是必不可少的和明确的：（i）与标准Borel设置中的Blackwell排序有部分相反，以及（ii）零和博弈中信息不完全的均衡存在性结果。