Substitution with Satiation: A New Class of Utility Functions and a Complementary Pivot Algorithm
提出一类新的效用函数和生产集（Leontief-free），适用于商品可替代且效用/生产次可加（建模商品间饱和）的情形，证明了均衡的存在性与计算复杂度，并给出了基于Lemke算法的互补枢轴算法，在商品数量固定时具有强多项式时间复杂性。
We introduce new classes of utility functions and production sets, called Leontief-free, which are applicable when goods are substitutes and utilities/production are subadditive (to model inter-good satiation). When goods are complements, the well studied Leontief utility functions do an adequate job; however, to the best of our knowledge, a similar concept for the case of goods that are substitutes was not known. For markets with these utility functions and production sets, we obtain the following results: Rational-valued equilibria, despite the fact that these utility functions and production sets are nonseparable. We prove that the problem of computing an equilibrium is PPAD-complete, where PPAD stands for Polynomial Parity Arguments on Directed Graphs. We obtain complementary pivot algorithms based on a suitable adaptation of Lemke’s classic algorithm. Our algorithms run in strongly polynomial time if the number of goods is a constant, despite the fact that the set of solutions is disconnected. Experimental verification confirms that our algorithms are practical.