#FOLLOWING function computes maximax and maximin
#decision values assuming rows are actions in payoff matrix
mmax=function(payoff){
nact=nrow(payoff) #number of actions
nj=ncol(payoff) #number of states of nature

maxact=apply(payoff,1,max)  #find row maximum
minact=apply(payoff,1,min)
#maxact=rep(0,nact)  #initialize
#i=1
#while (i<=nact) {
#maxact[i]=max(payoff[i,])
#i=i+1}
print(maxact)
om=order(maxact)
print(c("maximax choice is action number=",om[length(om)]),q=F)
sortact=sort(maxact)  #optimistic criterion maximax
maximax=max(maxact)
print(minact)
om=order(minact)
maximin=max(minact)
print(maximin)
print(c("maximin choice is action number=",om[length(om)]),q=F)

list(maximax=maximax, maximin=maximin, maxact=maxact, minact=minact)
}
###  end mmax function


#FOLLOWING function computes minimax regret 
# max expected value and minimum expected regret
#decision values assuming rows are actions in payoff matrix
max.expvalue=function(payoff, prob){
if (sum(prob)!=1) print("ERROR in prob input to max.expvalue function")
nact=nrow(payoff) #number of actions
nj=ncol(payoff) #number of states of nature
colmax=apply(payoff,2,max)  #maximize by column
best= matrix(colmax,nact,nj,byrow=T)
print(best)
regret=best-payoff
print(regret)
maxreg=apply(regret,1,max) #now by row max
print("maximum regret values")
print(maxreg)
print(min(maxreg)) #minimize max regret
om=order(maxreg)
print(c("minimax Regret choice is action number=",om[1]),q=F)

wpayoff=payoff
wregret=regret
#for (j in 1:nj) {
#wpayoff[,j]=payoff[,j]*prob[j]
#wregret[,j]=regret[,j]*prob[j]
#}
wpayoff=payoff%*%diag(prob)
wregret=regret %*%diag(prob)

print(wpayoff)
print("weighted payoff above and weighted regret below")
print(wregret)
ev=rep(NA,nact)  #initialize
ereg=rep(NA,nact)  #initialize
for (i in 1:nact) {
ev[i]=sum(wpayoff[i,])
ereg[i]=sum(wregret[i,]) }
print(ev)
print("expected value above, expected regret below")
print(ereg)
print("ordered exp value for each action")
print(order(ev))
sortev=sort(ev)  #sorted expected values
maxev=max(ev)
minreg=min(ereg)
om=order(ev)
print(c("max Expected value choice is action number=",om[length(om)]),q=F)
om=order(ereg)
print(c("min expected Regret choice is action number=",om[1]),q=F)


list(maxev=maxev, ev=ev, maxev=maxev, minreg=minreg)
}
###  end max.expvalue function



#example from the powerpoint
payoff=matrix(c(200,90,40,  50,120,30,  -120,-30,20), 3,3)  #define data
mmax(payoff) #apply first function to these data
prob=c(.3,.5,.2) #define probabilities
max.expvalue(payoff,prob) #apply second function with probabilities