A Note on Kuhn's Theorem ∗

We revisit Kuhn’s classic theorem on mixed and behavior strategies in games. We frame Kuhn’s work in terms of two questions in decision theory: What is the relationship between global and local assessment of uncertainty? What is the relationship between global and local optimality of strategies? This note is a homage to Kuhn’s classic theorem on the replacement of mixed by behavior strategies in games [Ku050, Ku053]. It reframes Kuhn’s work as two results in decision theory—i.e., in the context of trees involving a decision maker and Nature. The motivation is to see the meaning of Kuhn’s work at this basic level. The decision-theoretic framing in this note is in accordance with the socalled epistemic approach to game theory. Under the epistemic approach, a game is a multi-player decision problem—more exactly, a collection of decision problems, one for each player. In line with decision theory, a player is assumed to form a (subjective) probability assessment over the strategies chosen by other players in the game, and to choose an optimal strategy under t