CEBrule: Constrained equal benefits rule

In AirportProblems: Analysis of Cost Allocation for Airport Problems

Constrained equal benefits rule

Description

CEBrule calculates the contribution vector selected by the CEB rule.

Usage

CEBrule(c)

Arguments

c	A numeric cost vector.

Details

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

\text{CEB}_i(c)=\text{max}\{c_i-\beta,\ 0\}

where \beta>0 is chosen so that \sum\limits^n_{i=1}\text{CEB}_i(c)=c_n.

This rule focuses on the benefits each agent receives from not having to fully cover their own needs, aiming to distribute them as equitably as possible, without any agent subsidizing another.

The contribution selected by the CEB rule for a problem c \in C^N coincides with the payoff vector assigned by the modified nucleolus.

Value

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

References

Hu, C.-C., Tsay, M.-H., and Yeh, C.-H. (2012). Axiomatic and strategic justifications for the constrained equal benefits rule in the airport problem. Games and Economic Behavior, 75, 185-197.

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

Sudhölter, P. (1997). The modified nucleolus: Properties and axiomatizations. International Journal of Game Theory, 26, 146-182.

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
CEBrule(c)

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