Substitution with Satiation: A New Class of Utility Functions and a Complementary Pivot Equilibrium Algorithm∗

We introduce classes of utility functions and production sets, called Leontief-free, which are applicable when goods are substitutes and utilities/production are sub-additive (to model intergood 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: • Proof of rationality, despite the fact that these utility functions and production sets are nonseparable. • Proof of PPAD-completeness. • Complementary pivot algorithms based on a suitable adaptation of Lemke’s classic algorithm. • A strongly polynomial bound on the running time of our algorithms if the number of goods is a constant, despite the fact that the set of solutions is disconnected. • Experimental verification, which confirms that our algorithms are practical. ∗Supported by NSF Grants CCF-0914732 and CCF-1216019.