| coreVertices {CoopGame} | R Documentation |
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
Author(s)
Franz Mueller
Jochen Staudacher jochen.staudacher@hs-kempten.de
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
library(CoopGame)
coreVertices(c(0,0,0,1,1,1,3))
#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))