SECrule: Sequential equal contributions rule

In AirportProblems: Analysis of Cost Allocation for Airport Problems

Sequential equal contributions rule

Description

SECrule calculates the contribution vector selected by the SEC rule.

Usage

SECrule(c)

Arguments

c	A numeric cost vector.

Details

For each c\in C^N and each i\in N, the sequential equal contributions rule is defined by

\text{SEC}_i=\frac{c_1}{n}+\frac{c_2-c_1}{n-1}+\dots+\frac{c_i-c_{i-1}}{n-i+1}

This rule is based on applying an equal division to each segment separately, so that all agents using a given segment contribute equally to its cost. Each agent's contribution is then obtained as a sum of terms, one for each of the segments they use.

The contribution selected by the SEC rule for a problem c \in C^N coincides with the payoff vector assigned by the Shapley value to the associated cost game v\in G^N, that is, \text{SEC}(c)=\text{Sh}(v).

Value

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

References

Chun, Y., Hu, C.-C., and Yeh, C. (2012). Characterizations of the sequential equal contributions rule for the airport problem. International Journal of Economic Theory, 8, 77-85.

Littlechild, S.C. and Owen, G. (1973). A simple expression for the Shapley value in a special case. Management Science, 20, 370-372.

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

See Also

basicrule, weightedrule, clonesrule, hierarchicalrule

Examples

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

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