Analysis of Cost Allocation for Airport Problems
Coalitional game associated with an airport problem
Cost vector associated with an airport game
Allocation rule
Core-center rule
Constrained equal benefits rule
Constrained equal contributions rule
Cloned agents in an airport problem
Cost vector with cloned agents
Allocation rule with cloned agents
Graphical evaluation of the contribution vectors
Constrained proportional rule
Allocation rule according to the agents' hierarchical order
Overview of the allocation rules
Overview of the allocation rules with cloned agents
Overview of the allocation rules according to the agents' hierarchical...
Overview of the weighted allocation rules
Verification of compliance with the no-subsidy constraints
Face games associated with an airport problem
Vertices and visualization of the NS set
Composition of the no-subsidy set
Graphical representation of the contribution vectors within the NS set
Priority family of rules
Sequential equal contributions rule
Sequential full contributions rule
Parametric family of rules
Slack maximizer rule
Weighted allocation rule
Airport problems, introduced by Littlechild and Owen (1973) <https://www.jstor.org/stable/2629727>, are cost allocation problems where agents share the cost of a facility (or service) based on their ordered needs. Valid allocations must satisfy no-subsidy constraints, meaning that no group of agents contributes more than the highest cost of its members (i.e., no agent is allowed to subsidize another). A rule is a mechanism that selects an allocation vector for a given problem. This package computes several rules proposed in the literature, including both standard rules and their variants, such as weighted versions, rules for clones, and rules based on the agents’ hierarchy order. These rules can be applied to various problems of interest, including the allocation of liabilities and the maintenance of irrigation systems, among others. Moreover, the package provides functions for graphical representation, enabling users to visually compare the outcomes produced by each rule, or to display the no-subsidy set. In addition, it includes four datasets illustrating different applications and examples of airport problems. For a more detailed explanation of all concepts, see Thomson (2024) <doi:10.1016/j.mathsocsci.2024.03.007>.