Assessing strategic risk

In recent decades, subjective probabilities have been increasingly applied to an adversary's choices in strategic games (SGs). In games against nature (GANs), the subjective probability of a state can be elicited from lotteries yielding utility 1 if that state obtains, 0 otherwise. But in SGs, making such a lottery available changes the game, and so the players' incentives. Here, we propose a definition of subjective probabilities in SGs that uses actually available strategies only. The definition applies also to GANs where the decision maker's options are restricted. The probabilities that emerge need not be unique, but expected utilities are unique.