Question 1

In a simultaneous-move game, if (Bottom, Left) is an equilibrium in dominant strategies, which inequality must be true given the payoff matrix below?

Player B
|         | Left | Right |
|---------|------|-------|
| Top     | a,b  | c,d   |
| Bottom  | e,f  | g,h   |

Accepted Answer

$$e \geq a$$ and $$g \geq c$$

Question 2

How many Nash equilibria are there in the following simultaneous-move game?

Player 2
|         | U   | D   |
|---------|-----|-----|
| L       | 1,1 | 0,1 |
| R       | 1,0 | 0,0 |

Accepted Answer

4

Question 3

Consider an integer game between two players: Marilyn and Noah. Each player announces a positive integer simultaneously. The payoffs are: the loser pays $$1 to the winner, and if both announce the same integer, both get 0. $$Does this game have a Nash equilibrium?

Accepted Answer

No

Question 4

In a simultaneous-move integer game between Marilyn and Noah, each can announce 1, 2, 3, or 4. The payoffs are: loser pays $$1 to winner, same integer means both get 0. $$Does Marilyn have a dominant strategy?

Accepted Answer

Yes

Question 5

Which statement is incorrect regarding maximin strategy in the integer game between Marilyn and Noah?

Payoff rules: loser pays $$1 to winner, same integer means both get 0.$$

Accepted Answer

Marilyn has no maximin strategy.

Question 6

In the simultaneous-move game below, if both players play their maximin strategies, what is the payoff profile?

Player 2
|         | U      | D      |
|---------|--------|--------|
| L       | -100,-1| 2,-0.5 |
| R       | 1,-1   | -0.5,-0.5 |

Accepted Answer

$$(-0.5, -0.5)$$

Question 7

Consider a sequential-move integer game between Marilyn and Noah (numbers 1-4). Marilyn announces first, Noah second. Payoff: loser pays $$1 to winner, same integer means both get 0. $$What is the subgame perfect Nash equilibrium payoff for Noah?

Accepted Answer

0

Question 8

Consider a sequential-move integer game between Marilyn and Noah (numbers 1, 2, 3, ...). Marilyn announces first, Noah second. Payoff: loser pays $$1 to winner, same integer means both get 0. $$What is the subgame perfect Nash equilibrium payoff for Noah?

Accepted Answer

1

Question 9

In a two-firm Bertrand competition with homogeneous goods, Firm 1 has $$MC_1 = 2$, Firm 2 has MC_2$ = 3. $$Which of the following is a Nash equilibrium in the Bertrand model?

(First dimension: price charged by Firm 1; second: price charged by Firm 2)

Accepted Answer

$$(2.99, 3)$$

Question 10

Which of the following statements about oligopoly models is correct?

Accepted Answer

The monopoly/cartel model results in the highest total profit.

Question 11

In a simultaneous-move game, what is a Nash equilibrium?

Accepted Answer

Each player chooses a strategy that is a best response to the other player's strategy.

Question 12

In the Stackelberg model of oligopoly, what distinguishes it from the Cournot model?

Accepted Answer

Firms set quantities sequentially, with one firm acting as a leader.

Question 13

Which of the following is true about equilibrium in maximin strategies?

Accepted Answer

Each player chooses the strategy that maximizes their worst-case payoff.

Question 14

In a Prisoners’ Dilemma, what is the relationship between dominant strategies and Pareto dominance?

Accepted Answer

The equilibrium in dominant strategies is always Pareto dominated.

Question 15

Which of the following is NOT a characteristic of a Nash equilibrium?

Accepted Answer

All players receive the highest possible payoff.

Question 16

In a sequential-move game, what method is used to find the subgame perfect Nash equilibrium?

Accepted Answer

Backward induction

Question 17

In the Bertrand model, what happens if one firm sets a price just below the other firm’s marginal cost?

Accepted Answer

The firm with the lower price captures the entire market.

Question 18

Which of the following statements about total welfare in oligopoly models is correct?

Accepted Answer

Total welfare is highest in the competitive/Bertrand model.

Question 19

If a player in a game has a dominant strategy, what does this mean?

Accepted Answer

The player’s strategy is always the best response, regardless of what the other player does.

Question 20

In a real-world scenario, two firms are competing in a Bertrand market. Firm 1 has $$MC_1 = 2$, Firm 2 has MC_2$ = 3. If $$Firm 1 sets a price of $$2.99$$ and Firm 2 sets a price of $$3$$, what is the outcome?

Accepted Answer

Firm 1 captures the entire market.

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