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This function checks if the given game is convex.
convexcheck(v, binary = FALSE, instance = FALSE)
TRUE
if the game is convex, FALSE
otherwise. If instance=TRUE
and the game is not convex, the function also returns the positions (binary order positions if binary=TRUE
; lexicographic order positions otherwise) of a pair of coalitions violating the Zumsteg convexity characterization.
A characteristic function, as a vector.
A logical value. By default, binary=FALSE
. Should be set to TRUE
if v
is introduced in binary order instead of lexicographic order.
A logical value. By default, instance=FALSE
.
A game
A game
Zumsteg, S. (1995). Non-cooperative aspects of cooperative game theory and related computational problems. PhD thesis, ETH Zurich.
strategicallyequivalentcheck, superadditivecheck
v1 <- c(5, 2, 2, 1, 8, 8, 6, 4, 3, 3, 12, 10, 10, 6, 14)
convexcheck(v1)
v2 <- c(0, 0, 0, 2, 2, 1, 3)
convexcheck(v2, binary = FALSE, instance = TRUE)
# How to check if a game is concave:
v.conc <- c(4, 3, 3, 2, 6, 6, 5, 5, 4, 4, 7, 6, 6, 6, 7) # concave game
convexcheck(-v.conc)
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