Affiliations: [a] School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, Shaanxi, PR China | [b] School of Management, Northwestern Polytechnical University, Xi’an, Shaanxi, China
Correspondence:
[*]
Corresponding author. Hao sun, School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, P.R. China. Tel.: +86 29 88495957; Fax: +86 29 88430033; E-mail: [email protected].
Abstract: This paper focuses on a new model to reach the existence of equilibrium in a pure exchange economy with fuzzy preferences (PXE-FP). The proposed model integrates exchange, consumption and the agent’s fuzzy preference in the consumption set. We set up a new fuzzy binary relation on the consumption set to evaluate the fuzzy preferences. Also, we prove that there exists a continuous fuzzy order-preserving function in the consumption set under certain conditions. The existence of a fuzzy competitive equilibrium for the PXE-FP is confirmed through a new result on the existence of fuzzy Nash equilibrium for fuzzy non-cooperative games. The payoffs of all strategy profiles for any agent are fuzzy numbers in fuzzy non-cooperative games. Finally, we show that the fuzzy competitive equilibrium could be characterized as a solution to an associated quasi-variational inequality, giving rise to an equilibrium solution.
