ClaimsProblems (version 1.0.0)

CD: Concede-and-divide rule

Description

This function returns the awards vector assigned by the concede-and-divide (CD) rule to a two-claimant problem.

Usage

CD(E, d, name = FALSE)

Value

The awards vector selected by the CD rule. If name = TRUE, the name of the function (CD) as a character string.

Arguments

E

The endowment.

d

The vector of two claims.

name

A logical value.

Details

Let \(E\ge 0\) be the endowment to be divided and \(d=(d_1,d_2)\in \mathbb{R}_+^2\) the vector of claims such that \(d_1+d_2 \ge E\).

The concede-and-divide rule (CD) first assigns to each of the two claimants the difference between the endowment and the other agent’s claim (or 0 if this difference is negative), and divides the remainder equally. That is, for each \(i\in \{1,2\}\), $$\text{CD}_i(E,d)=\max\{E-d_j,0\}+\frac{E-\max\{E-d_i,0\}-\max\{E-d_j,0\}}{2}.$$ Several rules are extensions of the concede-and-divide rule to general populations: AA, APRO, MO, RA, and Talmud.

References

Aumann, R. and Maschler, M., (1985). Game theoretic analysis of a bankruptcy problem from the Talmud. Journal of Economic Theory 36, 195–213.

Mirás Calvo,M.Á., Núñez Lugilde, I., Quinteiro Sandomingo, C., and Sánchez Rodríguez,E. (2025). On how the rules that extend the concede-and-divide principle differ for pairs of claimants. Preprint.

Thomson, W. (2019). How to divide when there isn't enough. From Aristotle, the Talmud, and Maimonides to the axiomatics of resource allocation. Cambridge University Press.

See Also

allrules, AA, APRO, MO, pathawards, RA, Talmud.

Examples

E=10
d=c(7,8)
CD(E,d)
# Talmud, RA, MO, APRO, and AA coincide with CD for two-claimant problems
Talmud(E,d)
RA(E,d)
MO(E,d)
APRO(E,d)
AA(E,d)