## ----eval=TRUE, echo=FALSE---------------------------------------------------- child_docs <- list.files(path="chapters",recursive = TRUE, pattern=".Rmd", full.names = TRUE) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) (v <- c(0,0,0,100,115,125,220)) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) (Maschler <- c(0,0,0,60,60,60,72)) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) v <- c(30,40,50,90,100,110,180) (w <- getZeroNormalizedGameVector(v)) ## ---- collapse=TRUE, eval=FALSE----------------------------------------------- # library(CoopGame) # v <- c(30,40,50,90,100,110,180) # (w01 <- getZeroOneNormalizedGameVector(v)) # ## [1] 0.0000000 0.0000000 0.0000000 0.3333333 0.3333333 # ## [6] 0.3333333 1.0000000 ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) (Maschler <- c(0,0,0,60,60,60,72)) createBitMatrix(n=3,Maschler) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) v <- c(3,4,5,9,10,11,18) (MC <- getMarginalContributions(v)) # Look at all the permutations computed MC$combinations # Look at the matrix of marginal values # corresponding to these permutations MC$marginal_values ## ---- collapse=TRUE----------------------------------------------------------- MC$marginal_values[2,] ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) v <- c(3,4,5,9,10,11,18) # Compute dual game vector (vStar <- getDualGameVector(v)) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) v <- c(3,4,5,9,10,11,18) # Compute utopia payoff vector for specified game v (M <- getUtopiaPayoff(v)) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) v <- c(2,3,4,8,9,10,13) # Compute minimal rights vector for specified game v (m <- getMinimalRights(v)) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) A <-c(3,4,5,9,10,11,18) x <-c(5,6,7) # Compute vector of excess coefficients for specified game v (ec <- getExcessCoefficients(A,x)) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) A <-c(3,4,5,9,10,11,18) # Compute vector of gap function coefficients for specified game v (gap <- getGapFunctionCoefficients(A)) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) A <-c(3,4,5,9,10,11,18) x <-c(5,6,7) # Compute vector of per capita excess coefficients for specified game v (ecpc <- getPerCapitaExcessCoefficients(A,x)) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) A <-c(3,4,5,9,10,11,18) x <-c(5,6,7) # Compute vector of propensities to disrupt for specified game v (propVec <- getVectorOfPropensitiesToDisrupt(A,x)) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) # Define a simple game A <-c(0,0,0,1,1,0,1) # Find the minimum winning coalitions getMinimumWinningCoalitions(A) # Find the coalitions where player 2 is critical getCriticalCoalitionsOfPlayer(2,A) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) A <-c(0,0,0,0.8,0.9,0,0.9) # Find the real gaining coalitions getRealGainingCoalitions(A) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) # The Maschler game Maschler <-c(0,0,0,60,60,60,72) # Find the unanimity coefficients for the Maschler game (unCoeff <- getUnanimityCoefficients(Maschler)) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) # Example from book by T. Driessen, p. 75 A=c(0,0,0,9,9,15,18) # Compute 1-cover of this 1-convex game (A1 <- getkCover(A,k=1)) ## ---- collapse=TRUE,eval=FALSE------------------------------------------------ # library(CoopGame) # bankruptcyGame(n=3,d=c(100,200,300),E=300) # ## $n # ## [1] 3 # ## # ## $d # ## [1] 100 200 300 # ## # ## $E # ## [1] 300 # ## # ## $v # ## [1] 0 0 0 0 100 200 300 ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) # First approach bankruptcyGameVector(n=3,d=c(100,200,300),E=300) # # Alternative approach bankruptcyGame(n=3,d=c(100,200,300),E=300)$v ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) bankruptcyGameValue(S=c(2,3),d=c(100,200,300),E=300) ## ---- collapse=TRUE, eval=FALSE----------------------------------------------- # library(CoopGame) # TVACosts=c(163520,140826,250096,301607,378821,367370,412584) # (tvaCostGame <- costSharingGame(n=3, TVACosts)) # ## $n # ## [1] 3 # ## # ## $Costs # ## [1] 163520 140826 250096 301607 378821 367370 412584 # ## # ## $v # ## [1] 0 0 0 2739 34795 23552 141858 # # # # Alternatively, generate and output only the corresponding game vector # (v <- costSharingGameVector(n=3, TVACosts)) # ## [1] 0 0 0 2739 34795 23552 141858 ## ---- collapse = TRUE--------------------------------------------------------- library(CoopGame) gloveGame(n=3,L=c(1,3),R=2)$v # # Equivalent alternative approach gloveGameVector(n=3,L=c(1,3),R=2) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) cardinalityGame(4)$v # # Equivalent alternative approach cardinalityGameVector(4) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) weightedVotingGame(n=3, w=c(3,5,4), q=8)$v # # Equivalent alternative approach weightedVotingGameVector(n=3, w=c(3,5,4), q=8) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) majoritySingleVetoGame(n=4, vetoPlayer=2)$v # # Equivalent alternative approach majoritySingleVetoGameVector(n=4, vetoPlayer=2) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) unanimityGame(n=4, T=c(1,4))$v # # Equivalent alternative approach unanimityGameVector(n=4, T=c(1,4)) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) apexGame(n=4, apexPlayer=2)$v # # Equivalent alternative approach apexGameVector(n=4, apexPlayer=2) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) dictatorGame(n=4, dictator=3)$v # # Equivalent alternative approach dictatorGameVector(n=4, dictator=3) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) divideTheDollarGame(3)$v # # Equivalent alternative approach divideTheDollarGameVector(3) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) A <-c(0,0,0,1,1,0,1) isSuperadditiveGame(A) ## ---- collapse=TRUE----------------------------------------------------------- # The following game is 2-convex library(CoopGame) alpha = 0.48 v=c(0,0,0,alpha,alpha,0,1) iskConvexGame(v,2) # The following game is not 2-convex library(CoopGame) alpha = 0.52 v=c(0,0,0,alpha,alpha,0,1) iskConvexGame(v,2) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) v <-c(0,0,0,1,1,0,1) imputationsetVertices(v) belongsToImputationset(c(0.7,0.3,0),v) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) v <-c(0,0,0,1,1,0,3) coreVertices(v) belongsToCore(c(1.7,1.3,0),v) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) Aumann2010Example<-c(120,60,40,30,120,120,120,60,60,40,120,120,120,60,120) shapleyValue(Aumann2010Example) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) v100 = bankruptcyGameVector(n=3,d=c(100,200,300),E=100) nucleolus(v100) v200 = bankruptcyGameVector(n=3,d=c(100,200,300),E=200) nucleolus(v200) v300 = bankruptcyGameVector(n=3,d=c(100,200,300),E=300) nucleolus(v300) ## ---- collapse=TRUE----------------------------------------------------------- library(CoopGame) TVACosts=c(163520,140826,250096,301607,378821,367370,412584) (v <- costSharingGameVector(n=3, TVACosts)) TVACosts[1:3] - gatelyValue(v) TVACosts[1:3] - shapleyValue(v) TVACosts[1:3] - nucleolus(v) TVACosts[1:3] - tauValue(v) ## ---- collapse=TRUE, eval=FALSE----------------------------------------------- # library(CoopGame) # v<-weightedVotingGameVector(n=5, w=c(6,4,1,1,1), q=9) # normalizedBanzhafIndex(v) # ## [1] 0.47368421 0.36842105 0.05263158 0.05263158 0.05263158 # deeganPackelIndex(v) # ## [1] 0.375 0.250 0.125 0.125 0.125 # publicGoodIndex(v) # ## [1] 0.3333333 0.1666667 0.1666667 0.1666667 0.1666667 # johnstonIndex(v) # ## [1] 0.52777778 0.38888889 0.02777778 0.02777778 0.02777778 # publicHelpIndex(v) # ## [1] 0.28125 0.25000 0.15625 0.15625 0.15625 # publicHelpChiIndex(v) # ## [1] 0.3234568 0.3003086 0.1254115 0.1254115 0.1254115 # # # # Now player 1 donates one vote to player 2 # v<-weightedVotingGameVector(n=5, w=c(5,5,1,1,1), q=9) # normalizedBanzhafIndex(v) # ## [1] 0.5 0.5 0.0 0.0 0.0 # deeganPackelIndex(v) # ## [1] 0.5 0.5 0.0 0.0 0.0 # publicGoodIndex(v) # ## [1] 0.5 0.5 0.0 0.0 0.0 # johnstonIndex(v) # ## [1] 0.5 0.5 0.0 0.0 0.0 # publicHelpIndex(v) # ## [1] 0.2857143 0.2857143 0.1428571 0.1428571 0.1428571 # publicHelpChiIndex(v) # ## [1] 0.3309524 0.3309524 0.1126984 0.1126984 0.1126984 ## ---- collapse=TRUE, eval=FALSE----------------------------------------------- # library(CoopGame) # v<-weightedVotingGameVector(n=10, w=c(9,8,7,0,1,1,1,1,1,1), q=23) # normalizedBanzhafIndex(v) # ## [1] 0.326633166 0.326633166 0.316582915 0.000000000 0.005025126 # ## [6] 0.005025126 0.005025126 0.005025126 0.005025126 0.005025126 # deeganPackelIndex(v) # ## [1] 0.2291667 0.2291667 0.1666667 0.0000000 0.0625000 0.0625000 # ## [7] 0.0625000 0.0625000 0.0625000 0.0625000 # publicGoodIndex(v) # ## [1] 0.18181818 0.18181818 0.09090909 0.00000000 0.09090909 # ## [6] 0.09090909 0.09090909 0.09090909 0.09090909 0.09090909 # johnstonIndex(v) # ## [1] 0.332692308 0.332692308 0.323076923 0.000000000 0.001923077 # ## [6] 0.001923077 0.001923077 0.001923077 0.001923077 0.001923077 # publicHelpIndex(v) # ## [1] 0.15312132 0.15312132 0.15076561 0.07656066 0.07773852 # ## [6] 0.07773852 0.07773852 0.07773852 0.07773852 0.07773852 # publicHelpChiIndex(v) # ## [1] 0.16914603 0.16914603 0.16780487 0.06991541 0.07066461 # ## [6] 0.07066461 0.07066461 0.07066461 0.07066461 0.07066461 # # # # Now player 1 donates one vote to player 4 # v<-weightedVotingGameVector(n=10, w=c(8,8,7,1,1,1,1,1,1,1), q=23) # normalizedBanzhafIndex(v) # ## [1] 0.32908163 0.32908163 0.32397959 0.00255102 0.00255102 # ## [6] 0.00255102 0.00255102 0.00255102 0.00255102 0.00255102 # deeganPackelIndex(v) # ## [1] 0.22222222 0.22222222 0.16666667 0.05555556 0.05555556 # ## [6] 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556 # publicGoodIndex(v) # ## [1] 0.16666667 0.16666667 0.08333333 0.08333333 0.08333333 # ## [6] 0.08333333 0.08333333 0.08333333 0.08333333 0.08333333 # johnstonIndex(v) # ## [1] 0.3329026701 0.3329026701 0.3281653747 0.0008613264 0.0008613264 # ## [6] 0.0008613264 0.0008613264 0.0008613264 0.0008613264 0.0008613264 # publicHelpIndex(v) # ## [1] 0.15338882 0.15338882 0.15219976 0.07728894 0.07728894 0.07728894 # ## [7] 0.07728894 0.07728894 0.07728894 0.07728894 # publicHelpChiIndex(v) # ## [1] 0.16941222 0.16941222 0.16881669 0.07033698 0.07033698 0.07033698 # ## [7] 0.07033698 0.07033698 0.07033698 0.07033698 ## ---- collapse=TRUE, eval=FALSE----------------------------------------------- # library(CoopGame) # v<-weightedVotingGameVector(n=8, w=c(277,198,68,40,39,27,15,68), q=367) # shapleyShubikIndex(v) # ## [1] 0.426190476 0.178571429 0.111904762 0.059523810 0.059523810 # ## [6] 0.045238095 0.007142857 0.111904762 # normalizedBanzhafIndex(v) # ## [1] 0.427272727 0.154545455 0.118181818 0.063636364 0.063636364 # ## [6] 0.045454545 0.009090909 0.118181818 # johnstonIndex(v) # ## [1] 0.621621622 0.129129129 0.077477477 0.033483483 0.033483483 # ## [6] 0.023273273 0.004054054 0.077477477 # deeganPackelIndex(v) # ## [1] 0.2222222 0.1066667 0.1488889 0.1211111 0.1211111 0.1011111 # ## [7] 0.0300000 0.1488889 # publicGoodIndex(v) # ## [1] 0.18518519 0.11111111 0.14814815 0.12962963 0.12962963 0.11111111 # ## [7] 0.03703704 0.14814815 ## ---- collapse=TRUE, fig.show=TRUE-------------------------------------------- library(CoopGame) v0=c(6,8,10,18,20,22,31) drawImputationset(v0, label=FALSE) drawReasonableSet(v0, colour="blue", holdOn=TRUE) drawCore(v0, holdOn=TRUE, colour="red") drawModiclus(v0, holdOn=TRUE, colour="black") ## ---- collapse=TRUE, fig.show=TRUE-------------------------------------------- library(CoopGame) v0=c(6,8,10,18,20,22,31) drawReasonableSet(v0, colour="blue") drawCore(v0, holdOn=TRUE, colour="red") drawModiclus(v0, holdOn=TRUE, colour="black") ## ---- collapse=TRUE, fig.show=FALSE, eval=FALSE------------------------------- # #library(CoopGame) # #A=c(0,0,0,0,8,8,8,8,8,8,12,12,12,12,22) # #drawWeberset(A, colour ="grey") # #drawCore(A, colour ="red", holdOn = TRUE)