# pathawards: The path of awards for two claimants In ClaimsProblems: Analysis of Conflicting Claims

## Description

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

## Usage

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

## Arguments

 `d` The vector of claims. `claimants` The two claimants. `Rule` The rule: AA, APRO, CE, CEA, CEL, DT, MO, PIN, PRO, RA, Talmud. `col` The color. `points` The number of values of the endowment to draw the path.

## Details

Let d, with d≥ 0, be a vector of claims and denote D=∑ di the sum of claims.

The path of awards of a rule R for two claimants i and j is the parametric curve:

p(E)={(Ri(E,d),Rj(E,d)): 0≤ E ≤ D}.

## Value

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

## 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.

 ``` 1 2 3 4 5 6 7 8 9 10``` ```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) ```