### Abstract

Original language | English |
---|---|

Pages (from-to) | 947-956 |

Number of pages | 10 |

Journal | European Journal of Operational Research |

Volume | 276 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Aug 2019 |

### Keywords

- Game theory
- Competition regulation
- Toll caps
- Nash equilibrium
- Wardrop equilibrium
- MULTICOMMODITY NETWORKS
- PRICE-COMPETITION
- EFFICIENCY
- ALGORITHM
- ANARCHY

### Cite this

*European Journal of Operational Research*,

*276*(3), 947-956. https://doi.org/10.1016/j.ejor.2019.01.059

}

*European Journal of Operational Research*, vol. 276, no. 3, pp. 947-956. https://doi.org/10.1016/j.ejor.2019.01.059

**Toll caps in privatized road networks.** / Harks, Tobias; Schroeder, Marc; Vermeulen, Dries.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Toll caps in privatized road networks

AU - Harks, Tobias

AU - Schroeder, Marc

AU - Vermeulen, Dries

N1 - data source: no data used

PY - 2019/8/1

Y1 - 2019/8/1

N2 - We consider a network pricing game on a parallel network with congestion effects in which link owners set tolls for travel so as to maximize profit. A central authority is able to regulate this competition by means of a (uniform) price cap. The first question we want to answer is how such a cap should be designed in order to minimize the total congestion. We provide an algorithm that finds an optimal price cap for networks with affine latency functions and a full support wardrop equilibrium. Second, we consider the induced network performance at an optimal price cap. We show that for two link networks with affine latency functions, the congestion costs at the optimal price cap are at most 8/7 times the optimal congestion costs. For more general latency functions, this bound goes up to 2 under the assumption that an uncapped nash equilibrium exists. However, in general such an equilibrium need not exist and this can be used to show that optimal price caps can induce arbitrarily inefficient flows.

AB - We consider a network pricing game on a parallel network with congestion effects in which link owners set tolls for travel so as to maximize profit. A central authority is able to regulate this competition by means of a (uniform) price cap. The first question we want to answer is how such a cap should be designed in order to minimize the total congestion. We provide an algorithm that finds an optimal price cap for networks with affine latency functions and a full support wardrop equilibrium. Second, we consider the induced network performance at an optimal price cap. We show that for two link networks with affine latency functions, the congestion costs at the optimal price cap are at most 8/7 times the optimal congestion costs. For more general latency functions, this bound goes up to 2 under the assumption that an uncapped nash equilibrium exists. However, in general such an equilibrium need not exist and this can be used to show that optimal price caps can induce arbitrarily inefficient flows.

KW - Game theory

KW - Competition regulation

KW - Toll caps

KW - Nash equilibrium

KW - Wardrop equilibrium

KW - MULTICOMMODITY NETWORKS

KW - PRICE-COMPETITION

KW - EFFICIENCY

KW - ALGORITHM

KW - ANARCHY

U2 - 10.1016/j.ejor.2019.01.059

DO - 10.1016/j.ejor.2019.01.059

M3 - Article

VL - 276

SP - 947

EP - 956

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 3

ER -