Description Usage Arguments Value Author(s) References Examples
View source: R/GamePropertySemiConvexity.R
isSemiConvexGame checks if a TU game is semiconvex.
A TU game is semiconvex if and only if the following conditions hold true:
The gap function of any single player i
is minimal among the gap
function values of coalitions S
containing player i
.
Also, the gap function itself is required to be nonnegative.
1 |
v |
Numeric vector of length 2^n - 1 representing the values of the coalitions of a TU game with n players |
TRUE
if the game is semiconvex, else FALSE
.
Jochen Staudacher jochen.staudacher@hs-kempten.de
Driessen T. and Tijs S. (1985) "The tau-value, the core and semiconvex games", Int. Journal of Game Theory 14(4), pp. 229–247
Driessen T. (1998) Cooperative Games, Solutions and Applications, Springer, p. 76
1 2 3 4 5 6 7 8 9 10 11 12 13 | library(CoopGame)
isSemiConvexGame(c(0,0,0,1,1,1,4))
#Example of a semiconvex game
library(CoopGame)
v1<-c(3,4,5,9,10,11,18)
isSemiConvexGame(v1)
#Example of a game which not semiconvex
library(CoopGame)
v2=c(1:7)
isSemiConvexGame(v2)
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