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

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  • Jugal Garg

    (Department of ISE, University of Illinois at Urbana–Champaign, Urbana, Illinois 61801)

  • Ruta Mehta

    (Department of Computer Science, University of Illinois at Urbana–Champaign, Urbana, Illinois 61801)

  • Vijay V. Vaziranic

    (Department of Computer Science, University of California, Irvine, Irvine, California 92697)

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.

Suggested Citation

  • Jugal Garg & Ruta Mehta & Vijay V. Vaziranic, 2018. "Substitution with Satiation: A New Class of Utility Functions and a Complementary Pivot Algorithm," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 996-1024, August.
  • Handle: RePEc:inm:ormoor:v:43:y:2018:i:3:p:996-1024
    DOI: 10.1287/moor.2017.0892
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    References listed on IDEAS

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    Cited by:

    1. Yang Zhan & Chuangyin Dang, 2021. "Computing equilibria for markets with constant returns production technologies," Annals of Operations Research, Springer, vol. 301(1), pages 269-284, June.

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