ClaimsProblems (version 1.0.0)

pathawards3: The path of awards for three claimants

Description

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

Usage

pathawards3(d, claimants, Rule, col = "red", points = 300)

Value

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

Arguments

d

The vector of claims.

claimants

Three claimants.

Rule

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

col

The colour of the path, by default, col="red".

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 three claimants \(i,j,k\in N\) is the parametric curve: $$p(E)=\Bigl\{(\mathcal{R}_i(E,d),\mathcal{R}_j(E,d),\mathcal{R}_k(E,d))\in \mathbb{R}^3:\;E\in[0,D]\Bigr\}.$$

See Also

pathawards, schedrule, schedrules, verticalruleplot.

Examples

d=c(2,4,7,8)
claimants=c(1,3,4)
Rule=Talmud
pathawards3(d,claimants,Rule)