belongsToImputationset {CoopGame}

Check if point is imputation

Description

belongsToImputationset checks if the point belongs to the imputation set

Usage

belongsToImputationset(x, v)

Arguments

x

numeric vector containing allocations for each player

v

Numeric vector of length 2^n - 1 representing the values of the coalitions of a TU game with n players

Value

TRUE for a point belonging to the imputation set and FALSE otherwise

Author(s)

Johannes Anwander [e-mail]

Jochen Staudacher [e-mail]

References

Peleg B. and Sudhoelter P. (2007) Theory of cooperative games, 2nd Edition, Springer, p. 20

Maschler M., Solan E. and Zamir S. (2013) Game Theory, Cambridge University Press, p. 674

Osborne M.J. and Rubinstein A. (1994) A Course in Game Theory, MIT Press, p. 278

Narahari Y. (2015) Game Theory and Mechanism Design, World Scientific Publishing, p. 407

Examples

library(CoopGame)
belongsToImputationset(x=c(1,0.5,0.5), v=c(0,0,0,1,1,1,2))


library(CoopGame)
v=c(0,1,2,3,4,5,6)

#Point belongs to imputation set:
belongsToImputationset(x=c(1.5,1,3.5),v)

#Point does not belong to imputation set:
belongsToImputationset(x=c(2.05,2,2),v)