R: Important Concepts of Cooperative Game Theory

# Important Concepts of Cooperative Game Theory

## Documentation for package ‘CoopGame’ version 0.2.2

- DESCRIPTION file
- User guides, package vignettes and other documentation

## Help Pages

A B C D E G H I J K M N P Q R S T U W

## -- 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)