##
**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 |

PDFBibTeX
XMLCite

\textit{Y. Lan} et al., Fuzzy Optim. Decis. Mak. 10, No. 3, 211--232 (2011; Zbl 1219.91059)

Full Text:
DOI

### References:

[1] | Bierbrauer F. (2009) A note on optimal income taxation, public goods provision and robust mechanism design. Journal of Public Economics 93: 667–670 |

[2] | Boadway R., Gahvari F. (2006) Optimal taxation with consumption time as a leisure or labor substitute. Journal of Public Economics 90: 1851–1878 |

[3] | Cui L., Zhao R., Tang W. (2007) Principal-agent problem in a fuzzy environment. IEEE Transactions on Fuzzy Systems 15: 1230–1237 · Zbl 05516314 |

[4] | Casas E., Mateos M., Raymond J. P. (2001) Pontryagin’s principle for the control of parabolic equations with gradient state constraints. Nonlinear Analysis 46: 933–956 · Zbl 0998.49014 |

[5] | Costantino F., Di Gravio G. (2009) Multistage bilateral bargaining model with incomplete information-A fuzzy approach. International Journal of Production Economics 117: 235–243 |

[6] | Chen C. M. (2009) A fuzzy-based decision-support model for rebuy procurement. International Journal of Production Economics 122: 714–724 |

[7] | Gibbard A. (1973) Manipulation of voting schemes: a general result. Econometrica 41: 587–602 · Zbl 0325.90081 |

[8] | Huang X. X. (2009) A review of credibilistic portfolio selection. Fuzzy Optimization and Decision Making 8: 263–281 · Zbl 1187.91200 |

[9] | Hamilton J., Slutsky S. (2007) Optimal nonlinear income taxation with a finite population. Journal of Economic Theory 132: 548–556 · Zbl 1142.91687 |

[10] | Ke H., Ma W., Gao X., Xu W. (2010) New fuzzy models for time-cost trade-off problem. Fuzzy Optimization and Decision Making 9: 219–231 · Zbl 1231.90235 |

[11] | Laffont J. J. (1987) Optimal taxation of a non-linear pricing monopolist. Journal of Public Economics 33: 137–155 |

[12] | Liu B., Liu Y. K. (2002) Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems 10: 445–450 |

[13] | Liu B. (2002) Theory and practice of uncertain programming. Physica-Verlag, Heidelberg, Germany · Zbl 1029.90084 |

[14] | Liu B. (2006) A survey of credibility theory. Fuzzy Optimization and Decision Making 5: 387–408 · Zbl 1133.90426 |

[15] | Lan Y., Liu Y. K., Sun G. J. (2009) Modeling fuzzy multi-period production planning and sourcing problem with credibility service levels. Journal of Computational and Applied Mathematics 231: 208–221 · Zbl 1167.90004 |

[16] | Lan Y., Liu Y. K., Sun G. J. (2010) An approximation-based approach for fuzzy multi-period production planning problem with credibility objective. Applied Mathematical Modelling 34: 3202–3215 · Zbl 1201.90068 |

[17] | Luhandjula M. K. (2007) Fuzzy mathematical programming: theory, applications and extension. Journal of Uncertain Systems 1: 124–136 |

[18] | Moresi S. (1998) Optimal taxation and firm formation: A model of asymmetric information. European Economic Review 42: 1525–1551 |

[19] | Mirrlees J. (1971) An exploration in the theory of optimum income taxation. Review of Economic Studies 38: 175–208 · Zbl 0222.90028 |

[20] | Nahmias S. (1978) Fuzzy variables. Fuzzy Sets and Systems 1: 97–110 · Zbl 0383.03038 |

[21] | Pedrycz W. (2007) Granular computing–the emerging paradigm. Journal of Uncertain Systems 1: 38–61 |

[22] | Parker S. C. (1999) The optimal linear taxation of employment and self-employment incomes. Journal of Public Economics 73: 107–123 |

[23] | Sun G. J., Liu Y. K., Lan Y. (2010) Optimizing material procurement planning problem by two-stage fuzzy programming. Computers and Industrial Engineering 58: 97–107 |

[24] | Tanaka H., Guo P., Zimmermann H. J. (2000) Possibility distribution of fuzzy decision variables obtained from possibilistic linear programming problems. Fuzzy Sets and Systems 113: 323–332 · Zbl 0961.90136 |

[25] | Wang C., Tang W., Zhao R. (2007) On the continuity and convexity analysis of the expected value function of a fuzzy mapping. Journal of Uncertain Systems 1: 148–160 |

[26] | Xue F., Tang W., Zhao R. (2008) The expected value of a function of a fuzzy variable with a continuous membership function. Computers and Mathematics with Applications 55: 1215–1224 · Zbl 1149.03041 |

[27] | Zimmermann H. J. (1985) Applications of fuzzy set theory to mathematical programming. Information Sciences 36: 29–58 · Zbl 0578.90095 |

[28] | Zadeh L. A. (1965) Fuzzy sets. Information and Control 8: 338–353 · Zbl 0139.24606 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.