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Infinite Supermodularity and Preferences

In: Game Theory - Applications in Logistics and Economy

Author

Listed:
  • Alain Chateauneuf
  • Vassili Vergopoulos
  • Jianbo Zhang

Abstract

This chapter studies the ordinal content of supermodularity on lattices. This chapter is a generalization of the famous study of binary relations over finite Boolean algebras obtained by Wong, Yao and Lingras. We study the implications of various types of supermodularity for preferences over finite lattices. We prove that preferences on a finite lattice merely respecting the lattice order cannot disentangle these usual economic assumptions of supermodularity and infinite supermodularity. More precisely, the existence of a supermodular representation is equivalent to the existence of an infinitely supermodular representation. In addition, the strict increasingness of a complete preorder on a finite lattice is equivalent to the existence of a strictly increasing and infinitely supermodular representation. For wide classes of binary relations, the ordinal contents of quasisupermodularity, supermodularity and infinite supermodularity are exactly the same. In the end, we extend our results from finite lattices to infinite lattices.

Suggested Citation

  • Alain Chateauneuf & Vassili Vergopoulos & Jianbo Zhang, 2018. "Infinite Supermodularity and Preferences," Chapters, in: Danijela Tuljak-Suban (ed.), Game Theory - Applications in Logistics and Economy, IntechOpen.
    • Handle: RePEc:ito:pchaps:154359
    DOI: 10.5772/intechopen.79150
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    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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