Question

1. When playing Rock-Paper-Scissors, each player has the strategies Rock, Paper, and Scissors (abbreviated as R, P, and S).

What strategy did each player choose in the strategy profile (P, S), and who won?

2. When playing Rock-Paper-Scissors, each player has the strategies Rock, Paper, and Scissors (abbreviated as R, P, and S).

How would Player 2's preferences rank the strategy profiles (P, R) and (S, S)?

Group of answer choices

They would be indifferent between (P, R) and (S, S).

They would prefer (P, R) more than (S, S).

They would prefer (P, R) less than (S, S)

3. 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.

When modeled using game theory, which of the following would be strategies in this game?

Group of answer choices

a. Avoid fights

b. Be passive

c. Be aggressive

d. Avoid wasting energy

4. When training for the upcoming season, a sports team can choose to train for overwhelming Offense, overwhelming Defense, or a Balance of the two. When they play a game against another team, their choices of training determine who is most likely to win. The payoffs from this "game of training choice" are given below:

		Beavers
		Offense	Balance	Defense
Ducks	Offense	0, 0	2, -2	1, -1
	Balance	-2, 2	0, 0	2, -2
	Defense	-1, 1	-2, 2	0, 0

In the space below, answer the following questions:

• Does this game contain any strictly dominated strategies? (You do not need to list them right now.)
• If so, perform IESDS until none are left. List the order in which you eliminated strategies.
• Does elimination alone reveal the Nash equilibrium of this game? If so, what is it?

Answer 1

1) In profile (P,S), S is a strictly dominant strategy. So, each player will choose strategy profile (P,P) and nobody will win.

2) For player 2, (P, R) means Player 1 chooses Paper and 2 chooses rock, in which he loses. Whereas in (S,S), nobody wins anything. So, player 2 will prefer (S,S) over (P,R)

3) 2 strategies will be: Be passive and Be aggressive

4) This game does not have any straictly dominated strategies. For each player, Offense always dominates Balance, except when the other player chooses Defence. Similarly, Balance always dominates Defence, except when other player chooses Offence. The nash equilibrium for this game is (Offence, Offence).