# Infinite Supermodularity and Preferences

*Alain Chateauneuf* (),
*Vassili Vergopoulos* and
*Jianbo Zhang*

A chapter in *Game Theory - Applications in Logistics and Economy* from IntechOpen

**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.

**Keywords:** supermodularity; ?-supermodularity; lattice; JEL Classifications: D11; D12; C65 (search for similar items in EconPapers)

**JEL-codes:** C7 (search for similar items in EconPapers)

**References:** Add references at CitEc

**Citations:** Track citations by RSS feed

**Downloads:** (external link)

https://www.intechopen.com/books/game-theory-appli ... rity-and-preferences (text/html)

**Related works:**

Journal Article: Infinite supermodularity and preferences (2017)

Working Paper: Infinite supermodularity and preferences (2016)

Working Paper: Infinite Supermodularity and Preferences (2015)

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:ito:pchaps:154359

**DOI:** 10.5772/intechopen.79150

Access Statistics for this chapter

More chapters in Chapters from IntechOpen

Bibliographic data for series maintained by Slobodan Momcilovic ().