CECrule: Constrained equal contributions rule

In AirportProblems: Analysis of Cost Allocation for Airport Problems

Constrained equal contributions rule

Description

CECrule calculates the contribution vector selected by the CEC rule.

Usage

CECrule(c)

Arguments

c	A numeric cost vector.

Details

Let N^i_{-}\{j\in N:c_j<c_i\}. For each c\in C^N and each i\in N, the constrained equal contributions rule is defined by

\text{CEC}_i(c)=\text{min}\left\{\dfrac{1}{r-i+1}\left(c_r-\sum\limits_{j\in N^i_{-}}\text{CEC}_j(c)\right):r=1,\dots,n\right\}.

This rule offers a different approach to achieving equality. Contributions are distributed as evenly as possible while ensuring compliance with the no-subsidy constraints.

The contribution selected by the CEC rule for a problem c \in C^N coincides with the payoff vector assigned by the Dutta-Ray solution (denoted by \text{EA}) to the associated airport game v\in G^N, that is, \text{CEC}(c)=\text{EA}(v).

Value

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

References

Aadland, D. and Kolpin, V. (1998). Shared irrigation costs: an empirical and axiomatic analysis. Mathematical Social Sciences, 35, 203-218.

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

See Also

SIGMArule, basicrule, weightedrule, clonesrule, hierarchicalrule

Examples

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

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