getCriticalCoalitionsOfPlayer: Compute critical coalitions of a player for simple games

In CoopGame: Important Concepts of Cooperative Game Theory

Description

getCriticalCoalitionsOfPlayer identifies all coalitions for one player in which that player is critical (within a simple game). These coalitions are characterized by the circumstance that without this player the other players generate no value (then also called a losing coalition) - therefore this player is also described as a critical player.

Usage

getCriticalCoalitionsOfPlayer(player, v)

Arguments

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

Value

A data frame containing all minimal winning coalitions for one special player

Author(s)

Johannes Anwander [e-mail]

Jochen Staudacher [e-mail]

References

Deegan J. and Packel E.W. (1978) "A new index of power for simple n-person games", Int. Journal of Game Theory 7(2), pp. 151–161

Examples

library(CoopGame)
getCriticalCoalitionsOfPlayer(2,v=c(0,0,0,0,0,1,1))


library(CoopGame)
v=c(0,1,0,1,0,1,1)

#Get coalitions where player 2 is critical:
getCriticalCoalitionsOfPlayer(2,v)
#Output are all coalitions where player 2 is involved.
#Observe that player 2 is dictator in this game.
#
#     V1 V2 V3 cVal bmRow
#  2  0  1  0    1     2
#  4  1  1  0    1     4
#  6  0  1  1    1     6
#  7  1  1  1    1     7

CoopGame documentation built on Aug. 24, 2021, 1:07 a.m.