A Characterization of Rationalizable Consumer Behavior
研究了任意数据集满足GARP与可被效用函数理性化之间的等价关系，并证明存在满足GARP的无限数据集无法被连续或凹的效用函数理性化。
For an arbitrary data set D = {(p, x)} ⊆ (ℝ+m∖ {0}) × ℝ+m, finite or infinite, it is shown that the following three conditions are equivalent: (a) D satisfies GARP; (b) D can be rationalized by a utility function; (c) D can be rationalized by a utility function that is quasiconcave, nondecreasing, and that strictly increases when all its coordinates strictly increase. Examples of infinite data sets satisfying GARP are provided for which every utility rationalization fails to be lower semicontinuous, upper semicontinuous, or concave. Thus condition (c) cannot be substantively improved upon.