The four types of uncertainty in games introduced above are conceptually important, but not necessarily exhaustive nor mutually exclusive. John Harsanyi, for instance, argued that all uncertainty about the structure of the game, that is all possible incompleteness in information, can be reduced to uncertainty about the payoffs (Harsanyi 1967–68). (This was later formalized and proved by Stuart and Hu 2002). In a similar vein, Kadane &amp; Larkey (1982) argue that only strategic uncertainty is relevant for the assessment of decision in game situations. Contemporary epistemic game theory takes the view that, although it may ultimately be reducible to strategic uncertainty, making higher-order uncertainty explicit can clarify a great deal of what interactive or strategic rationality means.