Q: If Jill cheats and Jack uses a tit-for-tat strategy, what is the formula for Jack's profit in the next period?

$$ \text{Jack's profit} = 1,500 $$

Question 1

In the context of repeated games, which of the following best describes a 'tit-for-tat' strategy?

Accepted Answer

A player mirrors the opponent's previous action in the next period.

Question 2

Suppose Jack and Jill are playing a repeated game where Jack uses a trigger strategy. If Jill cheats in the current period, what will Jack do in all future periods?

Accepted Answer

Jack will never cooperate again.

Question 3

If Jack employs a tit-for-tat strategy and Jill cooperates this period, how many gallons will Jack produce?

Accepted Answer

Jack will produce 30 gallons.

Question 4

Jack employs a tit-for-tat strategy. If Jill cheated last period, what will Jack's total profit equal this period?

Accepted Answer

$$ Jack's profit will be 1$$,500 $

Question 5

Which of the following is a key difference between a one-time game and a repeated game in oligopoly theory?

Accepted Answer

Players in a repeated game can use strategies based on the opponent's previous choices.

Question 6

Consider the following payoff matrix for Jack and Jill in a one-time game:

$$\begin{array}{c|c|c}
 & 	ext{Cooperate} & 	ext{Cheat} \
\hline
	ext{Cooperate} & (1800, 1800) & (1500, 2000) \
	ext{Cheat} & (2000, 1500) & (1600, 1600) \
\end{array}

If $$both players use a trigger strategy, what is the Nash equilibrium in the repeated game?

Accepted Answer

Both players will cooperate as long as neither cheats.

Question 7

Suppose Jill cheats in a repeated game and Jack uses a trigger strategy. What is the present value of Jack's future profits if the game is infinitely repeated and the discount factor is $$\delta$$?

Accepted Answer

$$ PV = \frac{1,500}{1-\delta} $$

Question 8

In a repeated oligopoly game, why might firms prefer to cooperate rather than cheat, even if cheating yields a higher one-time profit?

Accepted Answer

Because cheating leads to permanent loss of trust and lower future profits.

Question 9

If the discount factor $$\delta is $$close to 1 in a repeated game, what does this imply about the players' valuation of future payoffs?

Accepted Answer

Players value future payoffs almost as much as current payoffs.

Question 10

Suppose Jack and Jill are in a repeated game. If both use tit-for-tat strategies and one cheats, what is the likely outcome in the next period?

Accepted Answer

Both will cheat.

Question 11

Which of the following best explains why trigger strategies can sustain cooperation in repeated games?

Accepted Answer

Trigger strategies threaten permanent punishment for cheating, making cooperation more attractive.

Question 12

In a repeated game, if the present value of cooperating is greater than the present value of cheating, what should a rational player do?

Accepted Answer

Cooperate in every period.

Question 13

If Jill cheats and Jack uses a tit-for-tat strategy, what is the formula for Jack's profit in the next period?

Accepted Answer

$$ 	ext{Jack's profit} = 1,500 $$

Question 14

Which of the following is NOT a characteristic of a repeated game in microeconomics?

Accepted Answer

Players interact only once.

Question 15

Suppose the weekly profit from cooperation is $$1,800$$ and from cheating is $$2,000$$ for Jack. If the game is repeated infinitely and the discount factor is $$\delta = 0.9$$, what is the present value of Jack's profits if he always cooperates?

Accepted Answer

$$ PV = \frac{1,800}{1-0.9} = 18,000 $$

Question 16

In a real-world oligopoly, such as the oil industry, why might firms avoid cheating on a collusive agreement?

Accepted Answer

Because cheating can trigger retaliation and lower profits in future periods.

Question 17

If the payoff from cheating is higher than cooperating in a single period, under what condition will cooperation be sustained in a repeated game?

Accepted Answer

If the present value of future cooperation exceeds the one-time gain from cheating.

Question 18

Which strategy is most likely to result in mutual cooperation in a repeated prisoner's dilemma?

Accepted Answer

Tit-for-tat.

Question 19

If Jack and Jill both use tit-for-tat strategies and the game is repeated indefinitely, what is the likely long-term outcome?

Accepted Answer

They will both cooperate unless one cheats, in which case both will cheat until cooperation resumes.

Question 20

In a repeated game, what is the effect of a high discount factor $$\delta on $$the likelihood of cooperation?

Accepted Answer

It increases the likelihood of cooperation.

Repeated Games and Strategies in Oligopoly: Tit-for-Tat and Trigger Strategies

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