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, binary=FALSE.

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

airfieldgame

Examples

E <- 10
d <- c(2,4,7,8)
claimsgame(E,d)

[Package TUGLab version 0.0.1 Index]