Question 1

Which of the following best describes a dominant strategy in game theory?

Accepted Answer

A strategy that is optimal no matter what an opponent does.

Question 2

In the context of the Prisoner's Dilemma, which of the following statements is TRUE?

Accepted Answer

The equilibrium in dominant strategies is Pareto dominated by another feasible outcome.

Question 3

Consider the following payoff matrix for two firms (see $$image_1). $$Using the quick method for identifying Nash equilibria, how many Nash equilibria are there in pure strategies?

Accepted Answer

3

Question 4

Given the payoff matrix in $$image_1$$, which of the following is a Nash equilibrium?

Accepted Answer

$$(Q=64, Q=64)$$

Question 5

Which of the following statements about Nash equilibrium is correct?

Accepted Answer

A Nash equilibrium is a profile of strategies where each player is playing a best response to the other player’s strategy.

Question 6

In the Battle of the Sexes game, which of the following is TRUE?

Accepted Answer

There are two Nash equilibria, but no equilibrium in dominant strategies.

Question 7

Suppose Player 1’s strategies are U and D, and Player 2’s strategies are L and R, with the following payoffs (see $$image_4). $$What is the maximin strategy for Player 2?

Accepted Answer

L

Question 8

Given the matrix in $$image_4$$, does this game have an equilibrium in dominant strategies?

Accepted Answer

No, only Player 1 has a dominant strategy.

Question 9

Which of the following statements is TRUE regarding the relationship between equilibrium in dominant strategies and Nash equilibrium?

Accepted Answer

An equilibrium in dominant strategies is always a Nash equilibrium.

Question 10

Suppose Firm 1 is highly risk-averse and fears the worst-case scenario in the investment game (see study material). Which strategy is Firm 1 most likely to choose according to the maximin criterion?

Accepted Answer

Don’t Invest

Question 11

In a game where both players have the following payoffs: (Work, Work): $$(8,8)$$, (Work, Shirk): $$(8,2)$$, (Shirk, Work): $$(2,8)$$, (Shirk, Shirk): $$(10,10)$$, which of the following is TRUE?

Accepted Answer

Both (Work, Work) and (Shirk, Shirk) are Nash equilibria.

Question 12

Which of the following best describes a Pareto dominated outcome?

Accepted Answer

An outcome where at least one player can be made better off without making anyone worse off.

Question 13

If a game has no Nash equilibrium in pure strategies, what does this imply?

Accepted Answer

Players may need to randomize their strategies to achieve equilibrium.

Question 14

In the context of maximin strategies, which of the following is correct?

Accepted Answer

A maximin strategy maximizes the minimum gain that can be earned.

Question 15

Suppose in a duopoly, both firms choose output levels simultaneously. If both firms choose $$Q=48$$, what are their payoffs according to the matrix in $$image_1$$?

Accepted Answer

$$4.6, 4.6$$

Question 16

Which of the following is NOT a feature of the Prisoner's Dilemma?

Accepted Answer

The Nash equilibrium is always unique.

Question 17

In the investment game (see study material), what is the equilibrium in maximin strategies?

Accepted Answer

(Don’t Invest, Invest)

Question 18

If a player is using a best response to the other player’s strategy, what does this mean?

Accepted Answer

They are maximizing their payoff given the other player’s choice.

Question 19

Which of the following is a quick method to identify all Nash equilibria in a payoff matrix?

Accepted Answer

Underline the highest payoffs for each player in each column and row; outcomes with two underlines are Nash equilibria.

Question 20

In a game with the following payoffs for Player 1: by choosing A, the worst-case payoff is 3; by choosing B, the worst-case payoff is 5. What is Player 1’s maximin strategy?

Accepted Answer

B

Game Theory: Nash Equilibrium, Dominant and Maximin Strategies

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