## Abstract

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.

Original language | English (US) |
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Pages (from-to) | 996-1024 |

Number of pages | 29 |

Journal | Mathematics of Operations Research |

Volume | 43 |

Issue number | 3 |

DOIs | |

State | Published - Aug 2018 |

## Keywords

- Arrow-Debreu markets
- Complementary pivot algorithm
- LCP
- Leontief-free utilities
- Market equilibrium
- PPAD

## ASJC Scopus subject areas

- Mathematics(all)
- Computer Science Applications
- Management Science and Operations Research