A bilevel fuzzy principal-agent model for optimal nonlinear taxation problems

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.