Important Concepts of Cooperative Game Theory

Documentation for package ‘CoopGame’ version 0.2.2

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-- A --

absoluteHollerValue	Compute absolute Public Good value
absolutePublicGoodValue	Compute absolute Public Good value
absolutePublicHelpChiValue	Compute absolute Public Help value Chi
absolutePublicHelpThetaValue	Compute absolute Public Help value Theta
absolutePublicHelpValue	Compute absolute Public Help value Theta
absolutePublicHelpValueChi	Compute absolute Public Help value Chi
absolutePublicHelpValueTheta	Compute absolute Public Help value Theta
absolutePublicHelpValueXi	Compute absolute Public Help value Chi
absolutePublicHelpXiValue	Compute absolute Public Help value Chi
apexGame	Construct an apex game
apexGameValue	Compute value of a coalition for an apex game
apexGameVector	Compute game vector for an apex game

-- B --

bankruptcyGame	Construct a bankruptcy game
bankruptcyGameValue	Compute value of a coalition for a bankruptcy game
bankruptcyGameVector	Compute game vector for a bankruptcy game
banzhafValue	Compute Banzhaf value
baruaChakravartySarkarIndex	Compute Barua Chakravarty Sarkar index
belongsToCore	Check if point is core element
belongsToCoreCover	Check if point is core cover element
belongsToImputationset	Check if point is imputation
belongsToReasonableSet	Check if point is element of reasonable set
belongsToWeberset	Check if point is element of Weber Set

-- C --

cardinalityGame	Construct a cardinality game
cardinalityGameValue	Compute value of a coalition for a cardinality game
cardinalityGameVector	Compute game vector for a cardinality game
centroidCore	Compute centroid of core
centroidCoreCover	Compute centroid of the core cover
centroidImputationSet	Compute centroid of the imputation set
centroidReasonableSet	Compute centroid of reasonable set
centroidWeberSet	Compute centroid of Weber set
colemanCollectivityPowerIndex	Compute Coleman Power index of a Collectivity to Act
colemanInitiativePowerIndex	Compute Coleman Initiative Power index
colemanPreventivePowerIndex	Compute Coleman Preventive Power index
coreCoverVertices	Compute core cover vertices
coreVertices	Compute core vertices
costSharingGame	Construct a cost sharing game
costSharingGameValue	Compute value of a coalition for a cost game
costSharingGameVector	Compute game vector for a cost sharing game
createBitMatrix	create bit matrix

-- D --

deeganPackelIndex	Compute Deegan-Packel index
dictatorGame	Construct a dictator game
dictatorGameValue	Compute value of a coalition for a dictator game
dictatorGameVector	Compute game vector for a dictator game
disruptionNucleolus	Compute disruption nucleolus
divideTheDollarGame	Construct a divide-the-dollar game
divideTheDollarGameValue	Compute value of a coalition for a divide-the-dollar game
divideTheDollarGameVector	Compute game vector for a divide-the-dollar game
drawCentroidCore	draw centroid of the core for 3 or 4 players
drawCentroidCoreCover	draw centroid of core cover for 3 or 4 players
drawCentroidImputationSet	draw centroid of imputation set for 3 or 4 players
drawCentroidReasonableSet	draw centroid of reasonable set for 3 or 4 players
drawCentroidWeberSet	draw centroid of Weber set for 3 or 4 players
drawCore	Draw core for 3 or 4 players
drawCoreCover	Draw core cover for 3 or 4 players
drawDeeganPackelIndex	draw Deegan-Packel index for 3 or 4 players
drawDisruptionNucleolus	draw disruption nucleolus for 3 or 4 players
drawGatelyValue	draw Gately point for 3 or 4 players
drawImputationSet	Draw imputation set for 3 or 4 players
drawImputationset	Draw imputation set for 3 or 4 players
drawJohnstonIndex	Draw Johnston index for 3 or 4 players
drawModiclus	Draw modiclus for 3 or 4 players
drawNormalizedBanzhafIndex	draw normalized Banzhaf Index for 3 or 4 players
drawNormalizedBanzhafValue	draw normalized Banzhaf value for 3 or 4 players
drawNucleolus	Draw nucleolus for 3 or 4 players
drawPerCapitaNucleolus	Draw per capita nucleolus for 3 or 4 players
drawPrenucleolus	Draw prenucleolus for 3 or 4 players
drawProportionalNucleolus	Draw proportional nucleolus for 3 or 4 players
drawPublicGoodIndex	Draw Public Good index for 3 or 4 players
drawPublicGoodValue	Draw Public Good value for 3 or 4 players
drawPublicHelpChiIndex	Draw Public Help index Chi for 3 or 4 players
drawPublicHelpChiValue	Draw Public Help value Chi for 3 or 4 players
drawPublicHelpIndex	Draw Public Help index Theta for 3 or 4 players
drawPublicHelpValue	Draw Public Help value Theta for 3 or 4 players
drawReasonableSet	Draw reasonable set for 3 or 4 players
drawShapleyShubikIndex	Draw Shapley-Shubik index for 3 or 4 players
drawShapleyValue	Draw Shapley value for 3 or 4 players
drawSimplifiedModiclus	Draw simplified modiclus for 3 or 4 players
drawTauValue	Draw tau-value for 3 or 4 players
drawTijsValue	Draw tau-value for 3 or 4 players
drawWeberset	Draw Weber Set for 3 or 4 players

-- E --

equalPropensityToDisrupt

Compute equal propensity to disrupt

-- G --

gatelyPoint	Compute Gately point
gatelyValue	Compute Gately point
getCriticalCoalitionsOfPlayer	Compute critical coalitions of a player for simple games
getDualGameVector	Compute dual game vector
getEmptyParamCheckResult	getEmptyParamCheckResult for generating stucture according to parameter check results
getExcessCoefficients	Compute excess coefficients
getGainingCoalitions	Compute gaining coalitions of a TU game
getGapFunctionCoefficients	Compute gap function coefficients
getHarsanyiDividends	Compute unanimity coefficients of game
getkCover	Compute k-cover of game
getMarginalContributions	Compute marginal contributions
getMinimalRights	Compute minimal rights vector
getMinimalRightsVector	Compute minimal rights vector
getMinimalWinningCoalitions	Compute minimal winning coalitions in a simple game
getMinimumWinningCoalitions	Compute minimal winning coalitions in a simple game
getNumberOfPlayers	Get number of players
getPerCapitaExcessCoefficients	Compute per capita excess coefficients
getPlayersFromBitVector	Extract players from bit vector
getPlayersFromBMRow	Extract players from bit matrix row
getRealGainingCoalitions	Compute real gaining coalitions of game
getUnanimityCoefficients	Compute unanimity coefficients of game
getUtopiaPayoff	Compute utopia payoff vector of game
getUtopiaPayoffVector	Compute utopia payoff vector of game
getVectorOfPropensitiesToDisrupt	Compute vector of propensities to disrupt
getWinningCoalitions	Compute winning coalitions in a simple game
getZeroNormalizedGameVector	Compute 0-normalized game vector
getZeroOneNormalizedGameVector	Compute 0-1-normalized game vector
gloveGame	Construct a glove game
gloveGameValue	Compute value of a coalition for a glove game
gloveGameVector	Compute game vector for glove game

-- H --

hollerIndex	Compute Public Good index
hollerValue	Compute (normalized) Public Good value

-- I --

imputationSetVertices	Compute vertices of imputation set
imputationsetVertices	Compute vertices of imputation set
is1ConvexGame	Check if game is 1-Convex
isAdditiveGame	Check if game is additive
isBalancedGame	Check if game is balanced
isConstantSumGame	Check if game is constant-sum
isConstantsumGame	Check if game is constant-sum
isConvexGame	Check if game is convex
isDegenerateGame	Check if game is degenerate
isEssentialGame	Check if game is essential
isInEssentialGame	Check if game is degenerate
isInessentialGame	Check if game is degenerate
iskConvexGame	Check if game is k-Convex
isMonotonicGame	Check if game is monotonic
isNonnegativeGame	Check if game is nonnegative
isQuasiBalancedGame	Check if game is quasi-balanced
isSemiConvexGame	Check if game is semiconvex
isSimpleGame	Check if game is simple
isSuperAdditiveGame	Check if game is superadditive
isSuperadditiveGame	Check if game is superadditive
isSymmetricGame	Check if game is symmetric
isWeaklyConstantSumGame	Check if game is weakly constant-sum
isWeaklyConstantsumGame	Check if game is weakly constant-sum
isWeaklySuperAdditiveGame	Check if game is weakly superadditive
isWeaklySuperadditiveGame	Check if game is weakly superadditive
isZeroMonotonicGame	Check if game is weakly superadditive

-- J --

johnstonIndex

Compute Johnston index

-- K --

koenigBraeuningerIndex

Compute Koenig-Braeuninger index

-- M --

majoritySingleVetoGame	Construct a weighted majority game with a single veto player
majoritySingleVetoGameValue	Compute value of a coalition for a weighted majority game with a single veto player
majoritySingleVetoGameVector	Compute game vector for a weighted majority game with a single veto player
modiclus	Compute modiclus

-- N --

nevisonIndex	Compute Nevison index
nonNormalizedBanzhafIndex	Compute non-normalized Banzhaf index
nonNormalizedBanzhafValue	Compute Banzhaf value
normalizedBanzhafIndex	Compute normalized Banzhaf index
normalizedBanzhafValue	Compute normalized Banzhaf value
nucleolus	Compute nucleolus

-- P --

perCapitaNucleolus	Compute per capita nucleolus
Prenucleolus	Compute prenucleolus
prenucleolus	Compute prenucleolus
propensityToDisrupt	Compute propensity to disrupt
proportionalNucleolus	Compute proportional nucleolus
publicGoodIndex	Compute Public Good index
publicGoodValue	Compute (normalized) Public Good value
publicHelpChiIndex	Compute Public Help index Chi
publicHelpChiValue	Compute (normalized) Public Help value Chi
publicHelpIndex	Compute Public Help index Theta
publicHelpIndexChi	Compute Public Help index Chi
publicHelpIndexTheta	Compute Public Help index Theta
publicHelpIndexXi	Compute Public Help index Chi
publicHelpThetaIndex	Compute Public Help index Theta
publicHelpThetaValue	Compute Public Help value Theta
publicHelpValue	Compute Public Help value Theta
publicHelpValueChi	Compute (normalized) Public Help value Chi
publicHelpValueTheta	Compute Public Help value Theta
publicHelpValueXi	Compute (normalized) Public Help value Chi
publicHelpXiIndex	Compute Public Help index Chi
publicHelpXiValue	Compute (normalized) Public Help value Chi

-- Q --

quotaGame	Construct a weighted voting game
quotaGameValue	Compute value of a coalition for a weighted voting game
quotaGameVector	Compute game vector for a weighted voting game (aka quota game)

-- R --

raeIndex	Compute Rae index
rawBanzhafIndex	Compute raw Banzhaf Index
rawBanzhafValue	Compute raw Banzhaf Value
reasonableSetVertices	Compute vertices of reasonable set

-- S --

shapleyShubikIndex	Compute Shapley-Shubik index
shapleyValue	Compute Shapley value
simplifiedModiclus	Compute simplified modiclus
stopOnInconsistentEstateAndClaimsVector	Parameter Function stopOnInconsistentEstateAndClaimsVector
stopOnInvalidAllocation	Parameter Function stopOnInvalidAllocation
stopOnInvalidBoolean	Parameter Function stopOnInvalidBoolean
stopOnInvalidClaimsVector	Parameter Function stopOnInvalidClaimsVector
stopOnInvalidCoalitionS	Parameter Function stopOnInvalidCoalitionS
stopOnInvalidDictator	Parameter Function stopOnInvalidDictator
stopOnInvalidEstate	Parameter Function stopOnInvalidEstate
stopOnInvalidGameVector	Parameter Function stopOnInvalidGameVector
stopOnInvalidGrandCoalitionN	Parameter Function stopOnInvalidGrandCoalitionN
stopOnInvalidIndex	Parameter Function stopOnInvalidIndex
stopOnInvalidLeftRightGloveGame	Parameter Function stopOnInvalidLeftRightGloveGame
stopOnInvalidNChooseB	Parameter Function stopOnInvalidNChooseB
stopOnInvalidNumber	Parameter Function stopOnInvalidNumber
stopOnInvalidNumberOfPlayers	Parameter Function stopOnInvalidNumberOfPlayers
stopOnInvalidQuota	Parameter Function stopOnInvalidQuota
stopOnInvalidVetoPlayer	Parameter Function stopOnInvalidVetoPlayer
stopOnInvalidWeightVector	Parameter Function stopOnInvalidWeightVector
stopOnParamCheckError	stopOnParamCheckError - stop and create error message on error

-- T --

tauValue	Compute tau-value
tijsValue	Compute tau-value

-- U --

unanimityGame	Construct a unanimity game
unanimityGameValue	Compute value of a coalition for a unanimity game
unanimityGameVector	Compute game vector for a unanimity game

-- W --

webersetVertices	Compute vertices of Weber Set
weightedVotingGame	Construct a weighted voting game
weightedVotingGameValue	Compute value of a coalition for a weighted voting game
weightedVotingGameVector	Compute game vector for a weighted voting game (aka quota game)