Journal
MATHEMATICS OF OPERATIONS RESEARCH
Volume 43, Issue 3, Pages 996-1024Publisher
INFORMS
DOI: 10.1287/moor.2017.0892
Keywords
Arrow-Debreu markets; market equilibrium; Leontief-free utilities; LCP; complementary pivot algorithm; PPAD
Funding
- National Science Foundation [CCF-0914732, CCF-1216019]
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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.
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