R Notebook

payoff <- matrix(c(-10000, 30000, 40000,
                   120000, 140000, 120000,
                  250000, 250000, 200000,
                 380000, 360000, 280000), 
                 nrow=4, ncol=3, byrow=TRUE)
colnames(payoff) <- c("Technique A", "Technique B", "Technique C")
rownames(payoff) <- c("Demand 3,000", "Demand 4,000", "Demand 5,000", "Demand 6,000")
print(payoff)

             Technique A Technique B Technique C
Demand 3,000      -10000       30000       40000
Demand 4,000      120000      140000      120000
Demand 5,000      250000      250000      200000
Demand 6,000      380000      360000      280000

# (a) MaxiMax
maximax <- apply(payoff, 2, max)
opt_maximax <- which.max(maximax)
print(maximax )

Technique A Technique B Technique C 
     380000      360000      280000 

print(opt_maximax)

Technique A 
          1 

cat("MaxiMax: ", names(maximax[opt_maximax]), "\n")

MaxiMax:  Technique A 

# (b) MaxMin
maxmin <- apply(payoff, 2, min)
opt_maxmin <- which.max(maxmin)
print(maximax )

Technique A Technique B Technique C 
     380000      360000      280000 

print(opt_maxmin )

Technique C 
          3 

cat("maxmin : ", names(maxmin[opt_maxmin ]), "\n")

maxmin :  Technique C 

# (c) MinMax Regret
regret <- matrix(0, nrow=nrow(payoff), ncol=ncol(payoff))
for(i in 1:nrow(payoff)){
  best <- max(payoff[i, ])
  regret[i, ] <- best - payoff[i, ]
}
colnames(regret) <- colnames(payoff)
rownames(regret) <- rownames(payoff)
print(regret)

             Technique A Technique B Technique C
Demand 3,000       50000       10000       0e+00
Demand 4,000       20000           0       2e+04
Demand 5,000           0           0       5e+04
Demand 6,000           0       20000       1e+05

max_regret <- apply(regret, 2, max)
opt_minmax_regret <- which.min(max_regret)
print(max_regret )

Technique A Technique B Technique C 
      5e+04       2e+04       1e+05 

print(opt_minmax_regret)

Technique B 
          2 

cat("max_regret : ", names(max_regret[opt_minmax_regret]), "\n")

max_regret :  Technique B 

#(d) Laplace Criterion (Equal Likelihood)
laplace <- apply(payoff, 2, mean)
opt_laplace <- which.max(laplace)
print(laplace )

Technique A Technique B Technique C 
     185000      195000      160000 

print(opt_laplace )

Technique B 
          2 

cat("laplace : ", names(laplace [opt_laplace ]), "\n")

laplace :  Technique B 

# (e) Hurwicz Criterion (alpha = 0.4)
alpha <- 0.4
hurwicz <- alpha * apply(payoff, 2, max) + (1 - alpha) * apply(payoff, 2, min)
opt_hurwicz <- which.max(hurwicz)
print(hurwicz )

Technique A Technique B Technique C 
     146000      162000      136000 

print(opt_hurwicz  )

Technique B 
          2 

cat("hurwicz : ", names(hurwicz [opt_hurwicz  ]), "\n")

hurwicz :  Technique B