Given a claims problem, this function returns the associated pessimistic claims game.
claimsgame(E, d, binary = FALSE)The characteristic function of the pessimistic claims game, as a vector in binary order if binary=TRUE and in lexicographic order otherwise.
An endowment, as a positive number.
A vector of claims.
A logical value. By default, binary=FALSE.
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).
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.
airfieldgame
E <- 10
d <- c(2,4,7,8)
claimsgame(E,d)
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