Order-k Rationality

A decision maker (DM) may not perfectly maximize her preference over the feasible set. She may feel it is good enough to maximize her preference over a sufficiently large consideration set; or just require that her choice is sufficiently well-ranked (e.g., in the top quintile of options); or even endogenously determine a threshold for what is good enough, based on an initial sampling of the options. Heuristics such as these are all encompassed by a common theory of order-k rationality, which relaxes perfect optimization by only requiring choices from a set S to fall within the set’s top k(S) elements according to the DM’s preference ordering. Heuristics aside, this departure from rationality offers a natural way, in the classic ‘as if’ tradition, to gradually accommodate more choice patterns as k increases. We characterize the empirical content of order-k rationality (and related theories), and provide a tractable testing method which is comparable to the method of checking SARP.