Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Cost allocation problems on highways with grouped users

Marcos Gómez-Rodríguez, Laura Davila-Pena, Balbina Casas-Méndez

Abstract

One of the practical applications of cooperative transferable utility games involves determining the fee structure for users of a given facility, whose construction or maintenance costs need to be recouped. In this context, certain efficiency and equity criteria guide the considered solutions. This paper analyzes how to allocate the fixed costs of a highway among its users through tolls, considering that different classes of vehicles or travelers utilize the service. For this purpose, we make use of generalized highway games with a priori unions that represent distinct user groups, such as frequent travelers or truckers, who, due to enhanced bargaining power, often secure reductions in their fares in real-world scenarios. In particular, the Owen value, the coalitional Tijs value, and a new value termed the Shapley-Tijs value, are axiomatically characterized. Additionally, straightforward formulations for calculating these values are provided. Finally, the proposed methodology is applied to actual traffic data from the AP-9 highway in Spain.

Cost allocation problems on highways with grouped users

Abstract

One of the practical applications of cooperative transferable utility games involves determining the fee structure for users of a given facility, whose construction or maintenance costs need to be recouped. In this context, certain efficiency and equity criteria guide the considered solutions. This paper analyzes how to allocate the fixed costs of a highway among its users through tolls, considering that different classes of vehicles or travelers utilize the service. For this purpose, we make use of generalized highway games with a priori unions that represent distinct user groups, such as frequent travelers or truckers, who, due to enhanced bargaining power, often secure reductions in their fares in real-world scenarios. In particular, the Owen value, the coalitional Tijs value, and a new value termed the Shapley-Tijs value, are axiomatically characterized. Additionally, straightforward formulations for calculating these values are provided. Finally, the proposed methodology is applied to actual traffic data from the AP-9 highway in Spain.
Paper Structure (11 sections, 12 theorems, 47 equations, 2 figures, 7 tables)

This paper contains 11 sections, 12 theorems, 47 equations, 2 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Cost games and generalized highway problems
  4. Cost games and generalized highway problems with a priori unions (or a coalitional structure)
  5. Main results
  6. Owen value
  7. Coalitional Tijs value
  8. Shapley-Tijs value
  9. Characterization of coalitional values in generalized highway problems
  10. An application to the Spanish AP-9 highway
  11. Conclusions

Key Result

Proposition 2.1

Let $\Gamma=(N,K,C,T)\in \mathcal{H}^{*}$ be a generalized highway problem, $(N, c)$ its associated game, and $\Phi$ the Shapley value. Then, for all $i\in N$, with $N_{t}=\{j\in N \mid t\in T(j)\}$ the set of agents that use section $t$, for each $t\in K$.

Figures (2)

  • Figure 1: Sections of the AP-9 highway between A Coruña and Vigo.
  • Figure 2: Subsections used by three types of vehicles that travel through three highway sections.

Theorems & Definitions (33)

  • Definition 2.1: Sudholter2017, Sudholter2017
  • Proposition 2.1: Mosquera2007, Mosquera2007
  • Definition 2.2
  • Definition 2.3
  • Remark 2.1
  • Proposition 2.2: Mosquera2007, Mosquera2007
  • Definition 2.4
  • Theorem 2.1: Owen1977, Owen1977
  • Definition 2.5
  • Proposition 3.1
  • ...and 23 more