Fuzzy games with a countable space of actions and applications to systems of generalized quasi-variational inequalities

TL;DR

This paper introduces a fuzzy economy model with a countable action space, proving the existence of fuzzy equilibria and applying these results to systems of generalized quasi-variational inequalities and new random fixed point theorems.

Contribution

It develops a novel fuzzy economy framework with countable actions and establishes existence results for equilibria and solutions to complex inequalities and fixed point problems.

Findings

Existence of fuzzy equilibrium in the proposed model

Solutions for systems of generalized quasi-variational inequalities

New random fixed point theorems for countable metric spaces

Abstract

In this paper, we introduce an abstract fuzzy economy (generalized fuzzy game) model with a countable space of actions and we study the existence of the fuzzy equilibrium. As applications, two types of results are obtained. The first ones concern the existence of the solutions for systems of generalized quasi-variational inequalities with random fuzzy mappings which we define. The last ones are new random fixed point theorems for correspondences with values in complete countable metric spaces.