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

Consider the following payoff matrix for the Prisoners' Dilemma:

$$\begin{array}{c|cc}
 & 	ext{Confess} & 	ext{Deny} \
\hline
	ext{Confess} & (-5, -5) & (0, -20) \
	ext{Deny} & (-20, 0) & (-1, -1) \
\end{array}$$

What is the equilibrium in dominant strategies?

Accepted Answer

(Confess, Confess)

Question 3

Which of the following outcomes Pareto dominates (Confess, Confess) in the Prisoners' Dilemma?

Accepted Answer

(Deny, Deny)

Question 4

Suppose in a two-player game, the payoff profiles are (10, 20) and (10, 19). Which statement is true?

Accepted Answer

(10, 20) Pareto dominates (10, 19)

Question 5

In the 'Husband and Wife Clean' game with the following payoff matrix:

$$\begin{array}{c|cc}
 & 	ext{Clean} & 	ext{Don’t Clean} \
\hline
	ext{Clean} & (10, 10) & (0, 15) \
	ext{Don’t Clean} & (15, 0) & (2, 2) \
\end{array}$$

Does this game satisfy both features of a Prisoners' Dilemma?

Accepted Answer

Yes, both features are satisfied.

Question 6

Which of the following is NOT a necessary condition for a Nash equilibrium in a two-player game?

Accepted Answer

Each player must have a dominant strategy.

Question 7

In the Pig and Piglet game, the Piglet’s best response is to Wait regardless of the Pig’s action. What does this imply?

Accepted Answer

The Piglet has a dominant strategy.

Question 8

Given the following payoff matrix for the Pig and Piglet game:

$$\begin{array}{c|cc}
 & 	ext{Wait} & 	ext{Press} \
\hline
	ext{Wait} & (0, 0) & (10, -1) \
	ext{Press} & (1, 8) & (6, 2) \
\end{array}$$

Which of the following is a Nash equilibrium?

Accepted Answer

(Press, Wait)

Question 9

If a game does not have an equilibrium in dominant strategies, what can we conclude?

Accepted Answer

We may still be able to predict outcomes using Nash equilibrium.

Question 10

Which of the following statements about Pareto domination is correct?

Accepted Answer

An outcome Pareto dominates another if it makes at least one player better off and no player worse off.

Question 11

In the context of the Prisoners' Dilemma, why is the equilibrium in dominant strategies considered a 'bad' outcome for the players?

Accepted Answer

Because it is Pareto dominated by another feasible outcome.

Question 12

Suppose in a game, Player 1’s best response to Player 2’s strategy is not unique. What does this imply?

Accepted Answer

There may be multiple Nash equilibria.

Question 13

Which of the following is an example of a game that does NOT have an equilibrium in dominant strategies?

Accepted Answer

Rock-Paper-Scissors

Question 14

In the Pig and Piglet game, if the Piglet chooses to Press, what is the Pig’s best response?

Accepted Answer

Wait

Question 15

Which of the following statements about Nash equilibrium is FALSE?

Accepted Answer

A Nash equilibrium always maximizes the sum of players’ payoffs.

Question 16

Consider the following scenario: In a business partnership, both partners can either 'Invest' or 'Not Invest'. The payoffs are as follows:

$$\begin{array}{c|cc}
 & 	ext{Invest} & 	ext{Not Invest} \
\hline
	ext{Invest} & (8, 8) & (2, 10) \
	ext{Not Invest} & (10, 2) & (4, 4) \
\end{array}$$

Does this game have an equilibrium in dominant strategies?

Accepted Answer

No, neither player has a dominant strategy.

Question 17

If an outcome is not Pareto dominated by any other outcome, what is it called?

Accepted Answer

Pareto efficient

Question 18

In the context of real-world applications, which of the following is an example of a Prisoners' Dilemma situation?

Accepted Answer

Two firms deciding whether to collude or compete in pricing.

Question 19

Suppose in a game, the equilibrium in dominant strategies is not Pareto dominated by any other outcome. What does this imply?

Accepted Answer

The game is not a Prisoners' Dilemma.

Question 20

Which of the following best describes the relationship between dominant strategies and Nash equilibrium?

Accepted Answer

Every equilibrium in dominant strategies is a Nash equilibrium.

Game Theory: Dominant Strategies, Prisoners’ Dilemma, and Nash Equilibrium

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