We define the model of an abstract economy with differential (asymmetric) information and a measure space of agents. We generalize N. C. Yannelis's result (2007), considering that each agent is characterised by a random preference correspondence instead of having a random utility function. We establish two different equilibrium existence results.
In this paper, we introduce a Bayesian abstract fuzzy economy model, and we prove the existence of Bayesian fuzzy equilibrium. As applications, we prove the existence of the solutions for two types of random quasi-variational inequalities with random fuzzy mappings, and we also obtain random fixed point theorems. MSC: 58E35; 47H10; 91B50; 91A44 Keywords: Bayesian abstract fuzzy economy; Bayesian fuzzy equilibrium; incomplete information; random fixed point; random quasi-variational inequalities; random fuzzy mapping
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.
In this paper, we establish coincidence-like results in the case when the values of the correspondences are not convex. In order to do this, we define a new type of correspondences, namely properly quasi-convex-like. Further, we apply the obtained theorems to solve equilibrium problems and to establish a minimax inequality. In the last part of the paper, we study the existence of solutions for generalized vector variational relation problems. Our analysis is based on the applications of the KKM principle. We establish existence theorems involving new hypothesis and we improve the results of some recent papers.
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