ClaimsProblems (version 1.0.0)

pathawards: The path of awards for two claimants

Description

This function returns the graphical representation of the path of awards of any rule for a claims vector and a pair of claimants.

Usage

pathawards(d, claimants, Rule, col = "red", points = 201)

Value

The graphical representation of the path of awards of a rule for the given claims and a pair of claimants.

Arguments

d

The vector of claims.

claimants

Two claimants.

Rule

The rule: AA, APRO, CE, CEA, CEL, AV, DT, MO, PIN, PRO, RA, Talmud, RTalmud.

col

The colour.

points

The number of values of the endowment to draw the path.

Details

Let \(N=\{1,\ldots,n\}\) be the set of claimants, \(d\in \mathbb{R}_+^N\) a vector of claims and denote by \(D=\sum_{i \in N} d_i\) the sum of claims.

The path of awards of a rule \(\mathcal{R}\) for two claimants \(i,j\in N\) is the parametric curve: $$p(E)=\Bigl\{(\mathcal{R}_i(E,d),\mathcal{R}_j(E,d))\in \mathbb{R}^2:\;E\in[0,D]\Bigr\}.$$

References

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

pathawards3, schedrule, schedrules, verticalruleplot.

Examples

d=c(2,4,7,8)
claimants=c(1,2)
Rule=Talmud
pathawards(d,claimants,Rule)
# The path of awards of the concede-and-divide rule
pathawards(c(2,3),c(1,2),CD)
#The path of awards of the DT rule for d=(d1,d2) with d2<2d1
pathawards(c(1,1.5),c(1,2),DT,col="blue",points=1001)
#The path of awards of the DT rule for d=(d1,d2) with d2>2d1
pathawards(c(1,2.5),c(1,2),DT,col="blue",points=1001)