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A bilevel fuzzy principal-agent model for optimal nonlinear taxation problems. (English) Zbl 1219.91059

Summary: This paper presents a bilevel fuzzy principal-agent model for optimal nonlinear taxation problems with asymmetric information, in which the government and the monopolist are the principals, the consumer is their agent. Since the assessment of the government and the monopolist about the consumer’s taste is subjective, therefore, it is reasonable to characterize this assessment as a fuzzy variable. What’s more, a bilevel fuzzy optimal nonlinear taxation model is developed with the purpose of maximizing the expected social welfare and the monopolist’s expected welfare under the incentive feasible mechanism. The equivalent model for the bilevel fuzzy optimal nonlinear taxation model is presented and Pontryagin maximum principle is adopted to obtain the necessary conditions of the solutions for the fuzzy optimal nonlinear taxation problems. Finally, one numerical example is given to illustrate the effectiveness of the proposed model, the results demonstrate that the consumer’s purchased quantity not only relates with the consumer’s taste, but also depends on the structure of the social welfare.

MSC:

91B26 Auctions, bargaining, bidding and selling, and other market models
91B64 Macroeconomic theory (monetary models, models of taxation)
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
91A80 Applications of game theory
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