An overview of Stackelberg pricing in networks.

*(English)*Zbl 1146.91018Summary: The Stackelberg pricing problem has two levels of decision making: tariff setting by an operator, and then selection of the cheapest alternative by customers. In the network version, an operator determines tariffs on a subset of the arcs that he owns. Customers, who wish to connect two vertices with a path of a certain capacity, select the cheapest path. The revenue for the operator is determined by the tariff and the amount of usage of his arcs. The most natural model for the problem is a (bilinear) bilevel program, where the upper level problem is the pricing problem of the operator, and the lower level problem is a shortest path problem for each of the customers.

This paper contains a compilation of theoretical and algorithmic results on the network Stackelberg pricing problem. The description of the theory and algorithms is generally informal and intuitive. We redefine the underlying network of the problem, to obtain a compact representation. Then we describe a basic branch-and-bound enumeration procedure. Both concepts are used for complexity issues and for the development of algorithms: establishing NP-hardness, approximability, special cases solvable in polynomial time, and an efficient exact branch-and-bound algorithm.

This paper contains a compilation of theoretical and algorithmic results on the network Stackelberg pricing problem. The description of the theory and algorithms is generally informal and intuitive. We redefine the underlying network of the problem, to obtain a compact representation. Then we describe a basic branch-and-bound enumeration procedure. Both concepts are used for complexity issues and for the development of algorithms: establishing NP-hardness, approximability, special cases solvable in polynomial time, and an efficient exact branch-and-bound algorithm.

##### MSC:

91B24 | Microeconomic theory (price theory and economic markets) |

91B26 | Auctions, bargaining, bidding and selling, and other market models |

91A40 | Other game-theoretic models |

91A80 | Applications of game theory |

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\textit{S. van Hoesel}, Eur. J. Oper. Res. 189, No. 3, 1393--1402 (2008; Zbl 1146.91018)

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