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arXiv · 2003.08656

Existence of an equilibrium for pure exchange economy with fuzzy preferences

Xia Zhang·Hao Sun·Xuanzhu Jin·Moses Olabhele Esangbedo
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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.

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Xia Zhang, Hao Sun, Xuanzhu Jin, Moses Olabhele Esangbedo. 2020-03-19. Existence of an equilibrium for pure exchange economy with fuzzy preferences. https://doi.org/10.3233/jifs-191011

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