dynamicplot: Dynamic plot

In ClaimsProblems: Analysis of Conflicting Claims

Dynamic plot

Description

For each claimaint, it plots the awards of the chosen rules for a dynamic model with t periods.

Usage

dynamicplot(
  E,
  d,
  Rules,
  claimant,
  percentage,
  times,
  col = NULL,
  legend = TRUE
)

Arguments

E	The endowment.
d	The vector of claims
Rules	The rules: AA, APRO, CE, CEA, CEL, AV, DT, MO, PIN, PRO, RA, Talmud, RTalmud.
claimant	A claimant.
percentage	A number in (0,1).
times	Number of iterations.
col	The colours. If col=NULL then the sequence of default colours is: c("red", "blue", "green", "yellow", "pink", "orange", "coral4", "darkgray", "burlywood3", "black", "darkorange", "darkviolet").
legend	A logical value. The colour legend is shown if legend=TRUE.

Details

Let N=\{1,\ldots,n\} be the set of claimants, E\ge 0 the endowment to be divided and d\in \mathbb{R}_+^N the vector of claims such that \sum_{i \in N} d_i\ge E.

A vector x=(x_1,\dots,x_n) is an awards vector for the claims problem (E,d) if 0\le x \le d and satisfies the balance requirement, that is, \sum_{i=1}^{n}x_i=E.

A rule is a function that assigns to each claims problem (E,d) an awards vector, that is, a division between the claimants of the amount available.

The formal definitions of the main rules are given in the corresponding function help.

Given l a natural number, the function solves each claims problem in time t, which is (E_t,d), with E_t=(1-p)^t E, p\in(0,1) and t=1,\ldots,l.

Value

This function represents the awards proposed by different rules for a claimant if the resource decreases in each iteration by a given percentage.

References

Mirás Calvo, M.A., Núñez Lugilde, I., Quinteiro Sandomingo, C., and Sánchez-Rodríguez, E. (2023). An algorithm to compute the average-of-awards rule for claims problems with an application to the allocation of CO_2 emissions. Annals of Operations Research 336, 1435-1459.

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, pathawards, pathawards3, schedrule, schedrules.

Examples

E=10
d=c(2,4,7,8)
Rules=c(Talmud,RA,AA,PRO)
claimant=1
percentage=0.076
times=10
dynamicplot(E,d,Rules,claimant,percentage,times)

ClaimsProblems documentation built on April 4, 2025, 2:21 a.m.