Here we have
$$\left[\begin{array}{}8 &3 &0 &5\\ 0 & 4& 4& 1\end{array}\right]$$
and I heard col2
$$\left[\begin{array}{}3\\4\end{array}\right]$$
is dominated by col3
$$\left[\begin{array}{}0\\4\end{array}\right]$$
and reduced matrix is
$$\left[\begin{array}{}8 &0 &5\\
0 & 4& 1\end{array}\right]$$
but how come?
if every element of the matrix is less, then we can delete the column?
On
Are you sure it is game theory ? In my view it looks like a matrix in production theory. The values represent the input factors. Here you have 2 Input factors and 4 production Technologies. And it is always more efficient, if you need no units of input factor 1 and 4 units of input factor 2, than 3 units of input factor 1 and 4 of input factor 2.
Thus, the production vector 2 is not efficient. Only the production vectors 1,3 and 4 are efficient.
greetings,
calculus
On
I am assuming this is for a zero sum game. If so recall that when we represent the payoff matrix of a finite zero sum two person game we do in terms of the row player payoffs. Thus rows are payoffs receives, but columns are what column player must pay. Thus higher numbers are will be worse for column player since he will have to pay more. Now the reason why column 2 is dominated by column 3 is because we see if row player chooses row 2 column player is indifferent since would have to pay 4 either way, but if row player chooses row 1, column player would have to pay 3 (whatever that is in this context) versus not paying at all. So there is no reason why column player would ever choose use column 2 strategy since this he is always better off in choosing column 3 no matter what row player does
Thus the usual way to look at is this way when comparing rows you bigger numbers but when comparing columns you want smaller numbers
I do not think this is true. It is possibly the other way round, i.e, col 3 is weakly dominated by col 2.