SFCrule: Sequential full contributions rule

In AirportProblems: Analysis of Cost Allocation for Airport Problems

Sequential full contributions rule

Description

SFCrule calculates the contribution vector selected by the SFC rule.

Usage

SFCrule(c)

Arguments

c	A numeric cost vector.

Details

For each c\in C^N and each i\in N, let N^i_{-}=\{j\in N:c_j<c_i} and let N^i(c)\subseteq N be defined by N^i(c)=\{j\in N:c_j=c_i\}, the sequential full contribution rule is defined by

\text{SFC}_i(c)=\frac{c_i-\text{max}\{c_j:j\in N^i_{-}\}}{|N_i(c)|}

According to this rule, an agent does not assist other agents with smaller needs than his own in covering the costs they require, even though he uses the same segments they use (similarly, he does not receive any assistance in covering his own segmental cost from agents with greater needs than his, even though these agents also use his segment). If multiple agents have the same cost parameters, they equally share the cost of the common segment they use.

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

PRIORrule, basicrule, weightedrule, hierarchicalrule

Examples

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

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