PRIORrule: Priority family of rules

View source: R/PRIORrule.R

PRIORruleR Documentation

Priority family of rules

Description

PRIORrule calculates the contribution vector selected by a priority rule.

Usage

PRIORrule(c, order = NULL)

Arguments

c

A numeric cost vector.

order

A numeric vector indicating the priority order of agents when making contributions. By default, agents follow their original indexing and contribute accordingly.

Details

For each c \in C^N and each i \in N, a priority rule relative to \pi \in \Pi^N is defined by

\text{P}^{\pi}_i(c)=\text{max}\Big\{0,\ c_i-\text{max}\{c_j:\pi(j)<\pi(i)\}\Big\}.

In this rule, each agent contributes at a different step, so that each one pays all that is necessary until reaching the no-subsidy constraint. Consequently, the agents who arrive first cover the cost of all subsequent agents whose cost is lower.

Value

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

References

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

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

See Also

NSfaces, basicrule, hierarchicalrule

Examples

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

# Fluctuating order
c <- c(1, 3, 7, 10) # Cost vector
order <- c(2, 1, 4, 3) # Priority order
PRIORrule(c, order)


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