problemdata {ClaimsProblems}

Claims problem data

Description

The function returns to which of the following sub-domains the claims problem belongs to: the lower-half, higher-half, and midpoint domains. In addittion, the function returns the minimal rights vector, the truncated claims vector, the sum and the half-sum of claims.

Usage

problemdata(E, d, draw = FALSE)

Arguments

E

The endowment.

d

The vector of claims.

draw

A logical value.

Details

Let E\ge 0 be the endowment to be divided and d\in \mathcal{R}^n the vector of claims with d\ge 0 and such that D=\sum_{i=1}^{n} d_i\ge E, the sum of claims D exceeds the endowment.

The lower-half domain is the sub-domain of claims problems for which the endowment is less or equal than the half-sum of claims, E \le D/2.

The higher-half domain is the sub-domain of claims problems for which the endowment is greater or equal than the half-sum of claims, E \ge D/2.

The midpoint domain is the sub-domain of claims problems for which the endowment is equal to the half-sum of claims, E = D/2.

The minimal right of claimant i in (E,d) is whatever is left after every other claimant has received his claim, or 0 if that is not possible:

m_i(E,d)=\max\{0,E-d(N\backslash\{i\})\},\ i=1,\dots,n.

Let m(E,d)=(m_1(E,d),\dots,m_n(E,d)) be the vector of minimal rights.

The truncated claim of claimant i in (E,d) is the minimum of the claim and the endowment:

t_i(E,d)=\min\{d_i,E\},\ i=1,\dots,n.

Let t(E,d)=(t_1(E,d),\dots,t_n(E,d)) be the vector of truncated claims.

Value

The minimal rights vector; the truncated claims vector; the sum, the half-sum of the claims, and the class (lower-half, higher-half, and midpoint domains) to which the claims problem belongs. It returns cod = 1 if the claims problem belong to the lower-half domain, cod = -1 if it belongs to the higher-half domain, and cod = 0 for the midpoint domain. Moreover, if draw = TRUE a plot of the claims, from small to large in the interval [0,D], is given.

See Also

setofawards, allrules

Examples

E=10
d=c(2,4,7,8)
problemdata(E,d,draw=TRUE)