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

Monica Patriche

doi:10.1186/1687-1812-2014-124

Abstract

We introduce an abstract fuzzy economy (generalized fuzzy game) model with a countable space of actions, and we study the existence of fuzzy equilibrium. As application, we prove the existence of solutions for the systems of generalized quasi-variational inequalities with random fuzzy mappings, defined in this paper. Our results bring novelty to the current literature by considering random fuzzy mappings whose values are fuzzy sets over complete countable metric spaces.

Highlights

The classical abstract economy model as formalized by Borglin and Keiding [ ] or Shafer and Sonnenschein [ ] consists of a finite set of agents, each characterized by certain constraints and preferences, described by correspondences
The purpose of this paper is twofold. It extends the study of the abstract economy model with private information and a countable set of actions defined by the author in the fuzzy setting, by taking into account those situations in which the agents may have partial control over the actions they choose
The uncertainties derived by the individual character of the agents in election situations are described with the help of fuzzy random mappings, as defined by Huang [ ]

Summary

Introduction

The classical abstract economy (or generalized game) model as formalized by Borglin and Keiding [ ] or Shafer and Sonnenschein [ ] consists of a finite set of agents, each characterized by certain constraints and preferences, described by correspondences. This section is devoted to defining a new model of abstract fuzzy economy with private information and a countable set of actions and to proving the existence of fuzzy equilibrium. This model generalizes the one defined in [ ] by considering the fuzzy setting It is different from other models of abstract fuzzy economy with private information existent in the literature (see [ ] or [ ]), because the values of random fuzzy constraint mappings and of random fuzzy preference mappings are fuzzy sets over countable complete metric spaces and the theory of the distributions of correspondences is used. We emphasize that our arguments to the existence of fuzzy equilibrium are different from the approaches used in literature, since the modeling of the private information and the countable space of actions assumes a new setting.

Random quasi-variational inequalities with random fuzzy mappings

New types of systems of generalized quasi-variational inequalities