Choosing with unknown causal information: Action-outcome probabilities for decision making can be grounded in causal models
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 (prob-abilistic) level. The classical Theorems of von Neumann-Morgenstern and Savage provide a formal criterion for rational choice using purely 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 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 both in the known and the unknown case. Finally, as an application, we extend the well-known concept of Nash Equilibrium to the case in which causal information is considered by the players of a strategic game.