Let 2 0 1 3 be the payoff matrix for a game a Determine the

Let 2 0

1 3 be the payoff matrix for a game

a) Determine the minmax strategy for the row players. That is find the strategy for the row player that gives him the best possible outcome in the case where the column players picks the best counter strategy.

Solution

For the minimum strategy for row players

In row 1, choose (1,2) i.e. row 1 second element then the column player must choose the entry from column 2 which will be equal to 3

In row 2,choose (2,1) i.e. row 2 first element since the column player will have to choose the element 2

For the maximum strategy for row players

In row 1, choose (1,1) i.e. row 1 first element then the column player must choose the entry from column 1 which will be equal to 1

In row 2,choose (2,2) i.e. row 2 second element since the column player will have to choose the element 0

Hence in both these cases we satisfy the best possible pairing