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CoopGame (version 0.2.2)

Important Concepts of Cooperative Game Theory

Description

The theory of cooperative games with transferable utility offers useful insights into the way parties can share gains from cooperation and secure sustainable agreements, see e.g. one of the books by Chakravarty, Mitra and Sarkar (2015, ISBN:978-1107058798) or by Driessen (1988, ISBN:978-9027727299) for more details. A comprehensive set of tools for cooperative game theory with transferable utility is provided. Users can create special families of cooperative games, like e.g. bankruptcy games, cost sharing games and weighted voting games. There are functions to check various game properties and to compute five different set-valued solution concepts for cooperative games. A large number of point-valued solution concepts is available reflecting the diverse application areas of cooperative game theory. Some of these point-valued solution concepts can be used to analyze weighted voting games and measure the influence of individual voters within a voting body. There are routines for visualizing both set-valued and point-valued solutions in the case of three or four players.

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Version

Install

install.packages('CoopGame')

Monthly Downloads

245

Version

0.2.2

License

GPL-2

Maintainer

Jochen Staudacher

Last Published

August 23rd, 2021

Functions in CoopGame (0.2.2)

bankruptcyGame

Construct a bankruptcy game
Prenucleolus

Compute prenucleolus
belongsToCore

Check if point is core element
drawCentroidCore

draw centroid of the core for 3 or 4 players
bankruptcyGameValue

Compute value of a coalition for a bankruptcy game
bankruptcyGameVector

Compute game vector for a bankruptcy game
belongsToCoreCover

Check if point is core cover element
belongsToReasonableSet

Check if point is element of reasonable set
centroidWeberSet

Compute centroid of Weber set
drawCentroidCoreCover

draw centroid of core cover for 3 or 4 players
getPerCapitaExcessCoefficients

Compute per capita excess coefficients
drawPrenucleolus

Draw prenucleolus for 3 or 4 players
getNumberOfPlayers

Get number of players
drawPerCapitaNucleolus

Draw per capita nucleolus for 3 or 4 players
dictatorGame

Construct a dictator game
drawNucleolus

Draw nucleolus for 3 or 4 players
colemanCollectivityPowerIndex

Compute Coleman Power index of a Collectivity to Act
deeganPackelIndex

Compute Deegan-Packel index
drawNormalizedBanzhafValue

draw normalized Banzhaf value for 3 or 4 players
coreCoverVertices

Compute core cover vertices
absolutePublicGoodValue

Compute absolute Public Good value
baruaChakravartySarkarIndex

Compute Barua Chakravarty Sarkar index
banzhafValue

Compute Banzhaf value
centroidReasonableSet

Compute centroid of reasonable set
centroidImputationSet

Compute centroid of the imputation set
costSharingGameVector

Compute game vector for a cost sharing game
createBitMatrix

create bit matrix
divideTheDollarGameValue

Compute value of a coalition for a divide-the-dollar game
centroidCore

Compute centroid of core
coreVertices

Compute core vertices
dictatorGameValue

Compute value of a coalition for a dictator game
drawProportionalNucleolus

Draw proportional nucleolus for 3 or 4 players
divideTheDollarGameVector

Compute game vector for a divide-the-dollar game
getkCover

Compute k-cover of game
nucleolus

Compute nucleolus
normalizedBanzhafValue

Compute normalized Banzhaf value
getZeroOneNormalizedGameVector

Compute 0-1-normalized game vector
drawJohnstonIndex

Draw Johnston index for 3 or 4 players
drawPublicHelpIndex

Draw Public Help index Theta for 3 or 4 players
drawImputationset

Draw imputation set for 3 or 4 players
drawPublicHelpChiValue

Draw Public Help value Chi for 3 or 4 players
drawWeberset

Draw Weber Set for 3 or 4 players
publicHelpChiValue

Compute (normalized) Public Help value Chi
drawPublicGoodIndex

Draw Public Good index for 3 or 4 players
equalPropensityToDisrupt

Compute equal propensity to disrupt
getUnanimityCoefficients

Compute unanimity coefficients of game
getRealGainingCoalitions

Compute real gaining coalitions of game
iskConvexGame

Check if game is k-Convex
isConvexGame

Check if game is convex
perCapitaNucleolus

Compute per capita nucleolus
getUtopiaPayoff

Compute utopia payoff vector of game
isDegenerateGame

Check if game is degenerate
getVectorOfPropensitiesToDisrupt

Compute vector of propensities to disrupt
johnstonIndex

Compute Johnston index
propensityToDisrupt

Compute propensity to disrupt
proportionalNucleolus

Compute proportional nucleolus
getExcessCoefficients

Compute excess coefficients
getGainingCoalitions

Compute gaining coalitions of a TU game
stopOnInvalidBoolean

Parameter Function stopOnInvalidBoolean
stopOnInvalidClaimsVector

Parameter Function stopOnInvalidClaimsVector
publicHelpIndex

Compute Public Help index Theta
disruptionNucleolus

Compute disruption nucleolus
drawCentroidImputationSet

draw centroid of imputation set for 3 or 4 players
divideTheDollarGame

Construct a divide-the-dollar game
centroidCoreCover

Compute centroid of the core cover
stopOnInvalidAllocation

Parameter Function stopOnInvalidAllocation
stopOnInvalidGameVector

Parameter Function stopOnInvalidGameVector
publicGoodIndex

Compute Public Good index
stopOnInvalidEstate

Parameter Function stopOnInvalidEstate
stopOnInconsistentEstateAndClaimsVector

Parameter Function stopOnInconsistentEstateAndClaimsVector
dictatorGameVector

Compute game vector for a dictator game
getPlayersFromBMRow

Extract players from bit matrix row
drawCentroidReasonableSet

draw centroid of reasonable set for 3 or 4 players
getPlayersFromBitVector

Extract players from bit vector
drawShapleyShubikIndex

Draw Shapley-Shubik index for 3 or 4 players
unanimityGameValue

Compute value of a coalition for a unanimity game
imputationsetVertices

Compute vertices of imputation set
isConstantSumGame

Check if game is constant-sum
isBalancedGame

Check if game is balanced
gloveGameVector

Compute game vector for glove game
getDualGameVector

Compute dual game vector
drawShapleyValue

Draw Shapley value for 3 or 4 players
isSuperadditiveGame

Check if game is superadditive
stopOnInvalidLeftRightGloveGame

Parameter Function stopOnInvalidLeftRightGloveGame
getEmptyParamCheckResult

getEmptyParamCheckResult for generating stucture according to parameter check results
getMinimalRights

Compute minimal rights vector
getMinimumWinningCoalitions

Compute minimal winning coalitions in a simple game
absolutePublicHelpChiValue

Compute absolute Public Help value Chi
drawCentroidWeberSet

draw centroid of Weber set for 3 or 4 players
drawModiclus

Draw modiclus for 3 or 4 players
drawCore

Draw core for 3 or 4 players
drawNormalizedBanzhafIndex

draw normalized Banzhaf Index for 3 or 4 players
isSymmetricGame

Check if game is symmetric
weightedVotingGameValue

Compute value of a coalition for a weighted voting game
stopOnInvalidNChooseB

Parameter Function stopOnInvalidNChooseB
weightedVotingGameVector

Compute game vector for a weighted voting game (aka quota game)
unanimityGameVector

Compute game vector for a unanimity game
gloveGame

Construct a glove game
colemanInitiativePowerIndex

Compute Coleman Initiative Power index
belongsToWeberset

Check if point is element of Weber Set
cardinalityGame

Construct a cardinality game
absolutePublicHelpValue

Compute absolute Public Help value Theta
colemanPreventivePowerIndex

Compute Coleman Preventive Power index
costSharingGame

Construct a cost sharing game
drawPublicHelpChiIndex

Draw Public Help index Chi for 3 or 4 players
drawSimplifiedModiclus

Draw simplified modiclus for 3 or 4 players
drawPublicGoodValue

Draw Public Good value for 3 or 4 players
gloveGameValue

Compute value of a coalition for a glove game
drawCoreCover

Draw core cover for 3 or 4 players
costSharingGameValue

Compute value of a coalition for a cost game
drawDeeganPackelIndex

draw Deegan-Packel index for 3 or 4 players
is1ConvexGame

Check if game is 1-Convex
isAdditiveGame

Check if game is additive
nonNormalizedBanzhafIndex

Compute non-normalized Banzhaf index
publicGoodValue

Compute (normalized) Public Good value
normalizedBanzhafIndex

Compute normalized Banzhaf index
drawTauValue

Draw tau-value for 3 or 4 players
isNonnegativeGame

Check if game is nonnegative
drawDisruptionNucleolus

draw disruption nucleolus for 3 or 4 players
drawGatelyValue

draw Gately point for 3 or 4 players
isQuasiBalancedGame

Check if game is quasi-balanced
publicHelpChiIndex

Compute Public Help index Chi
nevisonIndex

Compute Nevison index
isSimpleGame

Check if game is simple
reasonableSetVertices

Compute vertices of reasonable set
isSemiConvexGame

Check if game is semiconvex
modiclus

Compute modiclus
drawReasonableSet

Draw reasonable set for 3 or 4 players
drawPublicHelpValue

Draw Public Help value Theta for 3 or 4 players
stopOnInvalidQuota

Parameter Function stopOnInvalidQuota
stopOnInvalidVetoPlayer

Parameter Function stopOnInvalidVetoPlayer
stopOnInvalidWeightVector

Parameter Function stopOnInvalidWeightVector
shapleyShubikIndex

Compute Shapley-Shubik index
stopOnParamCheckError

stopOnParamCheckError - stop and create error message on error
majoritySingleVetoGameVector

Compute game vector for a weighted majority game with a single veto player
isWeaklySuperadditiveGame

Check if game is weakly superadditive
isWeaklyConstantSumGame

Check if game is weakly constant-sum
majoritySingleVetoGameValue

Compute value of a coalition for a weighted majority game with a single veto player
publicHelpValue

Compute Public Help value Theta
gatelyValue

Compute Gately point
getCriticalCoalitionsOfPlayer

Compute critical coalitions of a player for simple games
raeIndex

Compute Rae index
getMarginalContributions

Compute marginal contributions
getGapFunctionCoefficients

Compute gap function coefficients
tauValue

Compute tau-value
stopOnInvalidNumber

Parameter Function stopOnInvalidNumber
shapleyValue

Compute Shapley value
simplifiedModiclus

Compute simplified modiclus
stopOnInvalidNumberOfPlayers

Parameter Function stopOnInvalidNumberOfPlayers
unanimityGame

Construct a unanimity game
getZeroNormalizedGameVector

Compute 0-normalized game vector
getWinningCoalitions

Compute winning coalitions in a simple game
isEssentialGame

Check if game is essential
isMonotonicGame

Check if game is monotonic
koenigBraeuningerIndex

Compute Koenig-Braeuninger index
stopOnInvalidCoalitionS

Parameter Function stopOnInvalidCoalitionS
rawBanzhafIndex

Compute raw Banzhaf Index
majoritySingleVetoGame

Construct a weighted majority game with a single veto player
rawBanzhafValue

Compute raw Banzhaf Value
stopOnInvalidDictator

Parameter Function stopOnInvalidDictator
stopOnInvalidIndex

Parameter Function stopOnInvalidIndex
stopOnInvalidGrandCoalitionN

Parameter Function stopOnInvalidGrandCoalitionN
weightedVotingGame

Construct a weighted voting game
webersetVertices

Compute vertices of Weber Set
apexGameValue

Compute value of a coalition for an apex game
apexGame

Construct an apex game
apexGameVector

Compute game vector for an apex game
belongsToImputationset

Check if point is imputation
cardinalityGameValue

Compute value of a coalition for a cardinality game
cardinalityGameVector

Compute game vector for a cardinality game