On the Core, Bargaining Set and the Set of Competitive Allocations of Fuzzy Exchange Economy with a Continuum of Agents

Abstract

In this paper, we present a new model closer to the real-life — called the fuzzy exchange economy with a continuum of agents (FXE-CA) — that combines fuzzy consumption and fuzzy initial endowment with the agent’s fuzzy preference in the fuzzy consumption set. To characterize the fuzzy competitive allocations of the FXE-CA, we define the indifference fuzzy core of a FXE-CA as the set of all fuzzy allocations that cannot be dominated by any coalition of agents. We also propose the Mas-Colell indifference fuzzy bargaining set, in which no coalition has a justified objection at a fuzzy allocation against any other coalition. Finally, we verify that the indifference fuzzy core and the indifference fuzzy bargaining set of a FXE-CA coincide with the set of all fuzzy competitive allocations under some conditions, respectively. This indicates that the agents unanimously distribute the fuzzy competitive allocations of a FXE-CA.