# A Model of Mutual Learning in accordance with March (1991)
n<-50 # The number of individuals.
m<-30 # The number of dimensions.
p1<-0.1 # The socialization rate.
p2<-0.1 # The organization learning rate.
set.seed(501) # A random seed is 501.
# Reality has m dimensions.
# Each dimension has a value of -1 or 1 with independent equal probability 0.5.
r<-matrix(runif(m),1,m)
for(i in 1:m){ if(r[i] >= 0.5){ r[i]<- 1 }else{ r[i]<- -1} }
# Each of n individuals holds prior beliefs about reality.
# For each dimension of reality, each prior belief has a value of -1, 0, or 1 with equal probability 1/3.
b<-matrix(runif(n*m),n,m)
for(i in 1:n){ bP<-b[i,]
for(j in 1:m){if(bP[j] <= 0.3333333){ bP[j]<- -1
}else if(( bP[j]> 0.3333333) && (bP[j] <= 0.6666667)){ bP[j]<- 0
}else{ bP[j]<- 1 }
b[i,j]<-bP[j] }}
# CKL is the knowledge level of the organization code.
C<-matrix(rep(0),1,m)
CKLC<-function(C,r){ TrC<-0
for(i in 1:m){ if(C[,i] == r[,i]){ TrC<- TrC+1 } }
CKL<- TrC/m ; return(CKL) }
CKL<-CKLC(C,r)
# MKL is the knowledge level of individuals.
MKL<-matrix(rep(0),n,1)
MKLC<-function(b,r){
for(j in 1:n){ TrC<-0 ; B<-b[j,]
for(i in 1:m){ if(B[i] == r[,i]){ TrC<- TrC+1 } }
MKL[j,]<- TrC/m } ; return(MKL)}
MKL<-MKLC(b,r)
MKLA<-matrix(rep(0),1,80) # The average of individual knowledge levels of all 80 periods.
EQAR<-matrix(rep(0),1,80) # The equilibrium rate of all 80 periods.
# EQWI is 1 (equilibrium) if all the beliefs of the organization code and individuals are equal.
EQWI<-function(b,C){ TrEN<-0 ; TrE<-0
for(j in 1:n){ B<-b[j,]
for(i in 1:m){ if(B[i] == C[,i]){ TrE<- TrE+1 } }
}
nm<-n*m ; if(TrE == nm){ TrEN<-1 } ; return(TrEN)}
SG<-matrix(rep(0),1,n) # The ith dimension is 1 if the ith member belongs to the superior group.
SGB<- matrix(rep(2),1,m) # The initial value is 2, which means no dominant belief within the superior group.
# Individuals modify their beliefs as a consequence of socialization into the organization code.
B<-matrix(rep(0),n,m)
# Individual beliefs, code belief, and superior group belief at each period.
BT<-NULL
CT<-NULL
SGBT<-NULL
# The simulation starts.
t<-1 # The number of periods. t <= 80.
while(t <= 80){
## Individuals learn from the organization code.
# If the code is 0 on a particular dimension, then individual belief is not affected.
# If the code differs on any particular dimension from the individual belief,
# then individual belief changes to that of the code with probability p1 (when A is below p1).
for(j in 1:n){
for(i in 1:m){ if((C[i] != 0) && (C[i] != b[j,i])){ A<-runif(1) }else{ A<- 1.1 } ; if(A <= p1){ b[j,i] <- C[i] } }
}
# The superior group is composed of individuals whose knowledge levels are superior to that of the code.
for(j in 1:n){ MKLB<-MKL[j,] ; if(MKLB > CKL){ SG[,j] <- 1 }else{ SG[,j] <- 0 } }
# Individuals are selected from the superior group.
SGb<-cbind(b,t(SG)) ; SGb<-subset(SGb,SGb[,m+1] == 1) ; SGb<-SGb[,1:m] ; SGN<-sum(SG)
if(SGN != 0){ SGbN <- matrix(rep(0),m,3)
# The number of individual beliefs within superior group.
if(SGN != 1){ for(j in 1:SGN){ SGb2<-SGb[j,]
for(i in 1:m){ if(SGb2[i] == -1){ SGbN[i,1]<-SGbN[i,1]+1
}else if(SGb2[i] == 0){ SGbN[i,2]<-SGbN[i,2]+1
}else{ SGbN[i,3]<-SGbN[i,3]+1 } }
}
}else{SGb2<-SGb ; for(i in 1:m){ if(SGb2[i] == -1){ SGbN[i,1]<-SGbN[i,1]+1
}else if(SGb2[i] == 0){ SGbN[i,2]<-SGbN[i,2]+1
}else{ SGbN[i,3]<-SGbN[i,3]+1 } }
}
# SGN is dominant belief within the superior group.
for(i in 1:m){ if((SGbN[i,1] <= SGbN[i,2]) && (SGbN[i,2] < SGbN[i,3])){ SGB[1,i] <- 1
}else if((SGbN[i,2] <= SGbN[i,1]) && (SGbN[i,1] < SGbN[i,3])){ SGB[1,i] <- 1
}else if((SGbN[i,1] <= SGbN[i,3]) && (SGbN[i,3] < SGbN[i,2])){ SGB[1,i] <- 0
}else if((SGbN[i,3] <= SGbN[i,1]) && (SGbN[i,1] < SGbN[i,2])){ SGB[1,i] <- 0
}else if((SGbN[i,2] <= SGbN[i,3]) && (SGbN[i,3] < SGbN[i,1])){ SGB[1,i] <- -1
}else if((SGbN[i,3] <= SGbN[i,2]) && (SGbN[i,2] < SGbN[i,1])){ SGB[1,i] <- -1
}else{ SGB[1,i] <- 2 #if there is no dominant belief }
}
# Calculation of k.
k<-matrix(rep(0),1,m)
for(i in 1:m){
if(C[i] == 1){ NM<-SGbN[i,2]+SGbN[i,1] ; MM<-SGbN[i,3] ; k[i] <- NM - MM
}else if(C[i] == 0){ NM<-SGbN[i,1]+SGbN[i,3] ; MM<-SGbN[i,2] ; k[i] <- NM - MM
}else if(C[i] == -1){ NM<-SGbN[i,2]+SGbN[i,3] ; MM<-SGbN[i,1] ; k[i] <- NM - MM }
}
## The organization code adapts to the individual beliefs within the superior group.
for(i in 1:m){if((SGB[,i] != 2) && (C[,i] != SGB[,i]) && (k[,i] > 0)){
A<-runif(1) ; q<- 1- (1-p2)^k[,i] ; if(A <= q){ C[,i] <- SGB[,i] }
} }
}
}
CKL<-CKLC(C,r) #Knowledge level of the code after adaptation.
MKL<-MKLC(b,r) #Knowledge level of individuals after socialization.
MKLA[1,t]<-sum(MKL)/n #Average knowledge level of individuals after socialization.
# Calculation of equilibrium rate.
eqm<-0
for(j in 1:n){ b2<-b[j,]
for(i in 1:m){ if(b2[i] == C[,i]){ eqm<-eqm+1 } }
}
EQAR[1,t]<-eqm/(n*m)
BT[[t]]<-b
CT[[t]]<-C
SGBT[[t]]<-SGB
t<-t+1
}
# Print
MKLA
EQAR
EQWI(b,C)