CoopGame (version 0.2.2)

coreVertices: Compute core vertices

Description

Calculates the core vertices for given game vector

Usage

coreVertices(v)

Arguments

v

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

Value

rows of the matrix are the vertices of the core

References

Gillies D.B. (1953) Some Theorems on n-person Games, Ph.D. Thesis, Princeton University Press.

Aumann R.J. (1961) "The core of a cooperative game without side payments", Transactions of the American Mathematical Society 98(3), pp. 539--552

Peleg B. and Sudhoelter P. (2007) Theory of cooperative games, 2nd Edition, Springer, pp. 27--49

Maschler M., Solan E. and Zamir S. (2013) Game Theory, Cambridge University Press, pp. 686--747

Osborne M.J. and Rubinstein A. (1994) A Course in Game Theory, MIT Press, pp. 257--275

Examples

# NOT RUN {
library(CoopGame)
coreVertices(c(0,0,0,1,1,1,3))

# }
# NOT RUN {
#In the following case the core consists of a single point
v1 = c(0,1,2,3,4,5,6)
coreVertices(v1)
#     [,1] [,2] [,3]
#[1,]    1    2    3

#Users may also want to try the following commands:
coreVertices(c(0,0,0,60,80,100,135))
coreVertices(c(5,2,4,7,15,15,15,15,15,15,20,20,20,20,35))
coreVertices(c(0,0,0,0,0,5,5,5,5,5,5,5,5,5,5,15,15,15,15,15,15,15,15,15,15,30,30,30,30,30,60))
# }
# NOT RUN {
# }