| reasonableSetVertices {CoopGame} | R Documentation |
Compute vertices of reasonable set
Description
Calculates the vertices of the reasonable set for given game vector.
Usage
reasonableSetVertices(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 reasonable set
Author(s)
Jochen Staudacher jochen.staudacher@hs-kempten.de
References
Milnor J.W. (1953) Reasonable Outcomes for N-person Games, Rand Corporation, Research Memorandum RM 916.
Branzei R., Dimitrov D. and Tijs S. (2006) Models in cooperative game theory, Springer, p. 21
Chakravarty S.R., Mitra M. and Sarkar P. (2015) A Course on Cooperative Game Theory, Cambridge University Press, pp. 43–44
Gerard-Varet L.A. and Zamir S. (1987) "Remarks on the reasonable set of outcomes in a general coalition function form game", Int. Journal of Game Theory 16(2), pp. 123–143
Examples
library(CoopGame)
reasonableSetVertices(c(0,0,0,1,1,1,2))
library(CoopGame)
v <- c(0,0,0,3,3,3,6)
reasonableSetVertices(v)
# [,1] [,2] [,3]
# [1,] 3 0 3
# [2,] 0 3 3
# [3,] 3 3 0