Decision-making under uncertainty and causal thinking are fundamental aspects of intelligent reasoning. Decision-making has been well studied when the available information is considered at the associative (probabilistic) level. The classical Theorems of von Neumann-Morgenstern and Savage provide a formal criterion for rational choice using associative information: maximize expected utility. There is an ongoing debate around the origin of probabilities involved in such calculation. In this work, we will show how the probabilities for decision-making can be grounded in causal models by considering decision problems in which the available actions and consequences are causally connected. In this setting, actions are regarded as an intervention over a causal model. Then, we extend a previous causal decision-making result, which relies on a known causal model, to the case in which the causal mechanism that controls some environment is unknown to a rational decision-maker. In this way, action-outcome probabilities can be grounded in causal models in known and unknown cases. Finally, as an application, we extend the well-known concept of Nash Equilibrium to the case in which the players of a strategic game consider causal information.
翻译:在不确定性和因果思维下的决策是明智推理的根本方面。当在联合(概率)一级考虑现有信息时,对决策进行了仔细的研究。冯纽曼-摩根斯特尔和萨瓦奇的古典理论提供了使用关联信息进行合理选择的正式标准:最大限度地发挥预期效用。正在围绕这种计算所涉及的概率来源进行辩论。在这项工作中,我们将通过考虑与现有行动和后果有因果关系的决策问题,表明决策的概率可以基于因果模型。在这一背景下,行动被视为对因果模型的干预。然后,我们将以前基于已知因果模型的因果决策结果扩大到控制某些环境的因果机制不为理性决策者所了解的情况。这样,行动结果的概率可以基于已知和未知的因果模型。最后,作为应用,我们将众所周知的Nash Equilicrium概念扩大到战略游戏参与者考虑因果信息的案件。