A bilevel model of taxation and its application to optimal highway pricing

We consider a bilevel model where the leader wants to maximize revenues from a taxation scheme, while the follower rationally reacts to those tax levels. We focus our attention on the special case of a toll-setting problem defined on a multicommodity transportation network. We show that the general problem is NP-complete, while particular instances are polynomially solvable. Numerical examples are given.

[1]  C. M. Shetty,et al.  The bilinear programming problem , 1976 .

[2]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[3]  E. Aiyoshi,et al.  A solution method for the static constrained Stackelberg problem via penalty method , 1984 .

[4]  Wayne F. Bialas,et al.  Two-Level Linear Programming , 1984 .

[5]  Jonathan F. Bard,et al.  An investigation of the linear three level programming problem , 1984, IEEE Transactions on Systems, Man, and Cybernetics.

[6]  Robert G. Jeroslow,et al.  The polynomial hierarchy and a simple model for competitive analysis , 1985, Math. Program..

[7]  Patrice Marcotte,et al.  Network design problem with congestion effects: A case of bilevel programming , 1983, Math. Program..

[8]  J. Morgan,et al.  e-regularized two-level optimization problems: approximation and existence results , 1988 .

[9]  D. White,et al.  A solution method for the linear static Stackelberg problem using penalty functions , 1990 .

[10]  Jonathan F. Bard,et al.  A Branch and Bound Algorithm for the Bilevel Programming Problem , 1990, SIAM J. Sci. Comput..

[11]  Pierre Hansen,et al.  New Branch-and-Bound Rules for Linear Bilevel Programming , 1989, SIAM J. Sci. Comput..

[12]  Masao Fukushima,et al.  Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems , 1992, Math. Program..

[13]  Benjamin F. Hobbs,et al.  A nonlinear bilevel model for analysis of electric utility demand-side planning issues , 1992, Ann. Oper. Res..

[14]  F. Leurent Cost versus time equilibrium over a network , 1993 .

[15]  Omar Ben-Ayed,et al.  Bilevel linear programming , 1993, Comput. Oper. Res..

[16]  A. Ackere The principal/agent paradigm: Its relevance to various functional fields , 1993 .

[17]  G. Anandalingam,et al.  A penalty function approach for solving bi-level linear programs , 1993, J. Glob. Optim..

[18]  Paul H. Calamai,et al.  Bilevel and multilevel programming: A bibliography review , 1994, J. Glob. Optim..

[19]  Bethany L. Nicholson,et al.  Mathematical Programs with Equilibrium Constraints , 2021, Pyomo — Optimization Modeling in Python.

[20]  J. Bard,et al.  Nondifferentiable and Two-Level Mathematical Programming , 1996 .

[21]  Patrice Marcotte,et al.  Exact and inexact penalty methods for the generalized bilevel programming problem , 1996, Math. Program..

[22]  Michael C. Ferris,et al.  Complementarity and variational problems : state of the art , 1997 .