claimsgame {TUGLab} | R Documentation |
Pessimistic claims game associated with a claims problem
Description
Given a claims problem, this function returns the associated pessimistic claims game.
Usage
claimsgame(E, d, binary = FALSE)
Arguments
E |
An endowment, as a positive number. |
d |
A vector of claims. |
binary |
A logical value. By default, |
Details
A claims problem is a triple (N,E,d)
where E\ge 0
is an amount to be distributed among a set N
of agents and d\in \mathbb{R}^{|N|}
is a vector of claims satisfying \sum_{i=1}^{n} d_i\ge E
.
Given a claims problem (N,E,d)
, its associated claims game, v_{E,d}\in G^N
, is defined by
v_{E,d}(S)=\max\{0, \; E-\sum_{i\in N\backslash S}d_i\}\text{ for all }S\in 2^N.
For further analysis and computational methods related to conflicting claims problems, see the ClaimsProblems package Sánchez Rodríguez et al. (2025).
Value
The characteristic function of the pessimistic claims game, as a vector in binary order if binary=TRUE
and in lexicographic order otherwise.
References
O’Neill, B. (1982). A problem of rights arbitration from the Talmud. Mathematical Social Sciences, 2, 345–371.
Sánchez Rodríguez, E., Núñez Lugilde, I., Mirás Calvo, M., & Quinteiro Sandomingo, C. (2025). ClaimsProblems: Analysis of Conflicting Claims. R package version 1.0.0.
https://CRAN.R-project.org/package=ClaimsProblems
See Also
Examples
E <- 10
d <- c(2,4,7,8)
claimsgame(E,d)