The given pay-off matrix is :

Bob is the column player and Amy is the row player. The first term of each cell represents Amy's pay-off from a particular strategy , while the second term represents bob's pay-off.
Both players will play a maximin strategy. A maximin strategy necessarily means that the players seek to maximize their minimum gain.

• When Amy chooses Zumba , her pay-offs are 10 ( when Bob also chooses Zumba ) and 2 ( when Bob chooses running).
• When Amy chooses Running , her pay-offs are 0 ( when Bob chooses Zumba) and 8 ( when Bob chooses Running ).

So , the pay-offs for Amy can be represented as :

• When Amy chooses Zumba , her minimum pay-off would be 2 (2<10)
• When Amy chooses Running , her minimum payoff would be 0 (0>8)

Thus , Amy would look to maximize her gains from among the minimum choices. She would choose Zumba because Zumba gives her a greater pay-off from among the minimum pay-offs.
So , by following the maximin strategy , optimal choice for Amy would be Zumba.

Now ,

• when Bob chooses Zumba , his pay-offs are 8 ( when Amy chooses Zumba) and 0(when Amy chooses Running)
• When Bob chooses running , his pay-offs are 2 ( when Amy chooses Zumba) and 10(when Amy chooses Running)

So , the pay-offs of Bob can be represented as :

• When Bob chooses Zumba , his minimum pay-off would be 0 (0<8)
• When Bob chooses Running , his minimum pay-off would be 2 ( 2< 10).

Thus , Bob would look to maximize his gains from among the minimum choices. He would choose Running because Running gives him a greater pay-off from among the minimum pay-offs.
So , by following the maximin strategy , optimal choice for Bob would be Running.
An outcome is set to be Pareto efficient if there exists no other outcome which would make at least one person better off without making at least one person worse off.
( Zumba , Running) is NOT Pareto efficient
Thus , the equilibirum of this game that occurs when both the players follow maximin strategy is (Zumba , Running) , giving pay-offs of (2,2).

An outcome is said to be Pareto efficient if there exists no other outcome that would make at least one person better off without making another person worse off.
The outcome of ( Zumba , Running ) is not Pareto efficient because it is possible to move to another set of strategies ( Zumba , Zumba) or ( Running , Running) that would each give both Amy and Bob higher pay-offs and would make both of them strictly better off. (10,8) > (2,2) and (8,10) > (2,2).
Thus , the equilibrium in maximin strategies is NOT Pareto efficient.

2. The pay-off matrix of the game is given as :

Player 1 is the row player and Player 2 is the column player. The first term of each cell represents Player 1's pay-off from a particular strategy while the second term represents Player 2's pay-off.
We indicate the optimal choices by underlinning them.

• When Player 1 chooses U , Player 2 chooses L because it gives him a higher pay-off. (10>2)
• When Player 1 chooses D , Player 2 still chooses L. (26>22)
• When Player 2 chooses L , Player 1 chooses U (10>2)
• When Player 2 chooses R , Player 1 still chooses U (26>22)

Clearly , Player 2 never chooses R irrespective of what player 1 chooses. And Player 1 never chooses D irrespective of what Player 2 chooses.
Thus , U is the strictly dominant strategy for Player 1 and L is the strictly dominant strategy for Player 2.
The Nash Equilibrium is (U,L) and the equilibrium pay-off is (10,10).
Thus , it is TRUE that the Nash Equilibirum in this game occurs in dominant strategies.

However , the Nash Equilibrium pay-off (10,10) is NOT Pareto efficient because it is possible to move to another set of strategies ( D, R) that gives strictly better pay-offs for both the players. ( 22,22) > (10,10)
So , YES : The equilbrium occurs in dominant strategies. And the equilibrium is not Pareto efficient.