basicrule: Allocation rule

In AirportProblems: Analysis of Cost Allocation for Airport Problems

Allocation rule

Description

basicrule calculates the contribution vector resulting from the payment allocation among the different agents using one of the various predefined rules.

Usage

basicrule(c, rule, a = NULL, order = NULL)

Arguments

c	A numeric cost vector.
rule	A character string specifying the rule to apply.The rules that can be selected are: "SFC", "SEC", "CEC", "CP", "CEB", "SM", "CC", "SIGMA" and "PRIOR".
a	A numeric value in the range [0,1], controlling the parameterization of the rule. It can only be defined when rule = "SIGMA". By default, a = 0.5.
order	A numeric vector indicating the priority order of agents when making contributions. It can only be defined when rule = "PRIOR". By default, agents follow their original indexing and contribute accordingly.

Details

A rule is a mapping \mathcal{R}:C^N\rightarrow \mathbb{R}^N which associates with each problem c\in C^N a cost allocation vector \mathcal{R}(c) such that 0\leq\mathcal{R}(c)\leq c. In other words, a rule is a mechanism that selects for each airport problem an allocation vector.

The various proposed rules, despite their differences, share a key characteristic: for any given problem, each rule selects an allocation vector that belongs to its no-subsidy set. Although these rules have been individually characterized in different functions, the one in question encompasses all of them.

Value

A numeric contribution vector, where each element represents the payment of the different agents.

Note

When rule = "CC", the execution time of the function may significantly increase if the number of agents exceeds 150.

References

Bernárdez Ferradás, A., Mirás Calvo, M. Á., Quinteiro Sandomingo, C., and Sánchez-Rodríguez, E. (2025). Airport problems with cloned agents. [Preprint manuscript].

Potters, J. and Sudhölter, P. (1999). Airport problems and consistent allocation rules. Mathematical Social Sciences, 38, 83–102.

Thomson, W. (2024). Cost allocation and airport problems. Mathematical Social Sciences, 31(C), 17–31.

See Also

NSset, weightedrule, clonesrule, hierarchicalrule, multibasicrules

Examples

c <- c(1, 3, 7, 10) # Cost vector

# SEC rule
basicrule(c, rule = "SEC")

# PRIOR rule
order <- c(1, 3, 2, 4)
basicrule(c, "PRIOR", order = order)

AirportProblems documentation built on June 8, 2025, 10:49 a.m.