A new characterization of complete Heyting and co-Heyting algebras

TL;DR

This paper introduces a novel order-theoretic characterization of complete Heyting and co-Heyting algebras, revealing unexpected links to Nash equilibria through the Veinott ordering relation, with implications for supermodular game analysis.

Contribution

It provides a new characterization of complete Heyting and co-Heyting algebras using the Veinott ordering, connecting algebraic structures with game theory.

Findings

New order-theoretic characterization of complete Heyting and co-Heyting algebras.

Establishes a link between algebraic structures and Nash equilibria.

Highlights the role of Veinott ordering in understanding supermodular games.

Abstract

We give a new order-theoretic characterization of a complete Heyting and co-Heyting algebra $C$. This result provides an unexpected relationship with the field of Nash equilibria, being based on the so-called Veinott ordering relation on subcomplete sublattices of $C$, which is crucially used in Topkis' theorem for studying the order-theoretic stucture of Nash equilibria of supermodular games.