Question

Consider the following situation:

Two animals are competing for territory. Each animal chooses to be either Aggressive or Passive in this competition, and has the following preferences over the outcomes:

• Each animal would prefer to be Aggressive if the other is Passive: this way they win the competition and gain territory.
• Each animal would prefer to be Passive if the other is Aggressive: this way they lose territory, but they avoid a fight which would leave them injured.
• Regardless of whether an animal is Passive or Aggressive, they would prefer that their rival is Passive: dealing with an Aggressive rival costs energy and time that they could use for finding food.

Refer back to the situation in Question 4.

When modeled using game theory, how would Animal 1's preferences rank the four possible strategy profiles?

Group of answer choices

Most Preferred

      [ Choose ]            Animal 1 is Passive, Animal 2 is Aggressive            Animal 1 is Aggressive, Animal 2 is Aggressive            Animal 1 is Aggressive, Animal 2 is Passive.            Animal 1 is Passive, Animal 2 is Passive.      

2nd Most Preferred

      [ Choose ]            Animal 1 is Passive, Animal 2 is Aggressive            Animal 1 is Aggressive, Animal 2 is Aggressive            Animal 1 is Aggressive, Animal 2 is Passive.            Animal 1 is Passive, Animal 2 is Passive.      

3rd Most Preferred

      [ Choose ]            Animal 1 is Passive, Animal 2 is Aggressive            Animal 1 is Aggressive, Animal 2 is Aggressive            Animal 1 is Aggressive, Animal 2 is Passive.            Animal 1 is Passive, Animal 2 is Passive.      

Least Preferred

      [ Choose ]            Animal 1 is Passive, Animal 2 is Aggressive            Animal 1 is Aggressive, Animal 2 is Aggressive            Animal 1 is Aggressive, Animal 2 is Passive.            Animal 1 is Passive, Animal 2 is Passive.      

Refer back to the situation in Question 4.

When modeled using game theory, how would Animal 2's preferences rank the four possible strategy profiles?

Group of answer choices

Most Preferred

      [ Choose ]            (P, A)            (A, P)            (P, P)            (A, A)      

2nd Most Preferred

      [ Choose ]            (P, A)            (A, P)            (P, P)            (A, A)      

3rd Most Preferred

      [ Choose ]            (P, A)            (A, P)            (P, P)            (A, A)      

Least Preferred

      [ Choose ]            (P, A)            (A, P)            (P, P)            (A, A)      

Answer 1

Each player has two possible actions- 'Passive' and 'Aggressive'

The given information-

1. Each animal prefers that their opponent is passive irrespective of whether they are passive or aggressive.
2. When opponent is passive then the animal prefers to be aggressive because then the aggressive players wins territory
3. And when opponent is Aggressive then it prefers to be passive, as although lose territory but at least they are not injured by choosing not to fight.

The preference choices for both the animals are identical and determined as follows -

• As, point (1) suggest most preferred is opponent to passive. Thus, corresponding to it the player choice has either to be aggressive and passive. But the player will prefer being aggressive (as point 2 suggest) the most given the other player plays passive. As by choosing that it at least win the territory.
• The second most preferred would be being passive when opponent is passive. The reason behind it because player prefers their opponent is passive.
• Third most preferred will be being passive given that opponent is aggressive (as point (3) suggest) because by choosing that it at least prevent from being injured.
• And the least preferred will be being aggressive when opponent is aggressive.This is because then not known who will win the territory but for sure will be injured.

The actions available Passive (P) and Aggressive (A). The action pair is (Animal 1's action, Animal 2's action)

The preference choice of Animal 1 is as follows -

• The most preferred is animal 1 is Aggressive and animal 2 is passive (A, P).
• The second most preferred is both the animals are passive (P, P) .
• The third most preferred is animal 1 is passive and animal 2 is aggressive (P, A).
• The least preferred for animal 1 is both aggressive. (A, A).

That is preference order for Animal 1 is -

(A, P) > (P, P) > (P, A) > (A, A)

Similarly, similar will be the preference choice for Animal 2 only order changes that are -

• Animal 2's most preferred is (P, A).
• Animal 2' s second most preferred is (P, P).
• Animal 2's third most preferred is ( A, P ).
• And the least preferred is (A, A).

That is the preference order of Animal 2 is -

(P, A) > (P, P) > ( A, P ) > (A, A)