For each claimaint, it plots the awards of the chosen rules for a dynamic model with t periods.
dynamicplot(
E,
d,
Rules,
claimant,
percentage,
times,
col = NULL,
legend = TRUE
)This function represents the awards proposed by different rules for a claimant if the resource decreases in each iteration by a given percentage.
The endowment.
The vector of claims
The rules: AA, APRO, CE, CEA, CEL, AV, DT, MO, PIN, PRO, RA, Talmud, RTalmud.
A claimant.
A number in (0,1).
Number of iterations.
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").
A logical value. The colour legend is shown if legend=TRUE.
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 \(t=1,\ldots,l\).
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.
allrules, pathawards, pathawards3, schedrule, schedrules.
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)
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