Judging the Rationality of Decisions in the Presence of Vague Alternatives

The standard framework of the decision theory is subjected to partial revision in regard to the usage of the notion of alternative. An approach to judging the rationality of decision-maker's behavior is suggested for various cases of incomplete observability and/or controllability of alternatives. The approach stems from the conventional axiomatic treatment of rationality in the general choice theory and proceeds via modifying the description of alternative modes of behavior into a generalized model that requires no explicit consideration of alternatives. The criteria of rationality in the generalized decision model are proposed. For the conventional model in the choice theory, these criteria can be reduced to the well known criteria of the regularity (binariness) of choice functions. Game and economic examples are considered.