Decision theory, which combines probability theory with utility theory, provides a formal and complete framework for decisions (economic or otherwise) made under uncertainty— that is, in cases where probabilistic descriptions appropriately capture the decision maker’s environment.
This is suitable for “large” economies where each agent need pay no attention to the actions of other agents as individuals. For “small” economies, the situation is much more like a game: the actions of one player can significantly affect the utility of another (either positively or negatively).
Von Neumann and Morgenstern’s development of game GAME THEORY theory (see also Luce and Raiffa, 1957) included the surprising result that, for some games, a rational agent should adopt policies that are (or least appear to be) randomized. Unlike decision theory, game theory does not offer an unambiguous prescription for selecting actions.