Question

9. Use the following payoff matrix to answer the following questions.

Suppose this is a one-shot game:

a. Determine the dominant strategy for each player. If such strategies do not exist, explain why not.

b. Determine the secure strategy for each player. If such strategies do not exist, explain why not.

c. Determine the Nash equilibrium of this game. If such an equilibrium does not exist, explain why not

Short answer

a. Player 1's dominant strategy is option A and Player 2's dominant strategy is option C.

b. The secure strategy for player 1 will be option A while for player 2 it will be option C.

c. The Nash equilibrium is strategy A, C (-10,-10).

Step-by-step solution

Finding the dominant strategy

a.

Here, both players only have one opportunity to choose their option, in which each player will seek to make the decision that will generate the highest possible payoff, thus generating their dominant strategy.

With respect to the dominant strategy of player 1, if player 2 chooses C, it will be convenient for player 1 to choose A since it is the strategy that will generate the least loss (-10). On the other hand, if player 2 chooses option D, Player 1 will also choose option A since 200 is greater than 140 if he chooses B.

Thus, Player 1's dominant strategy is option A.

With respect to the dominant strategy of player 2 , if player 1 chooses A, it will be convenient for player 2 to choose C since it is the strategy that will generate the least loss (-10). Also, if player 1 chooses option B, player 2 will also choose option C since it will generate a higher payoff than option D(220,180).

Thus, Player 2's dominant strategy is option C.

Finding the secure strategy of each player

b.

The safe strategy of each player will be the one that will ensure the highest possible payoff in the worst possible scenario.

This strategy is used when there is no dominant strategy. Thus, the security strategy for player 1 will be option A while for player 2 it will be option C.

Finding the Nash equilibrium 

c.

Assuming that no player will win anything if he decides to change his strategy under the assumption that the other individuals do not change theirs, Player 1's most optimal strategy to Player 2's response will be option A, while Player's most optimal strategy 2 to Player l's response will be option C.

Therefore, the Nash equilibrium does exist in this game and it is strategy A, C (-10,-10).

It is important to mention that in this Nash equilibrium both players obtain losses, however in many cases the players would like to have an equilibrium with higher profits, only that there is a risk of being betrayed by the rival player.