Practice Worksheet

Chapter 17 — Oligopoly · based on Prof. Pac's Discussion Worksheet 12

Part 1

Short Answer — Quality Products vs. Perfection Performed

Setup Two firms — Quality Products and Perfection Performed — decide independently whether to run an advertising campaign.

If Quality advertises and Perfection does not: Quality earns $1,000, Perfection earns $0.
If both advertise: each earns $500.
If neither advertises: each earns $700.
Payoffs are symmetric (swap roles for the reverse case).

Question 1a — Complete the Payoff Matrix

Fill in each cell with the payoff for Quality Products (QP) and Perfection Performed (PP). Use dollars (no $ sign needed).

		Perfection Performed
		Advertise	Not Advertise
Quality Products	Advertise	QP $ PP $	QP $ PP $
Quality Products	Not Advertise	QP $ PP $	QP $ PP $

Hint Symmetric payoffs means the table mirrors across its diagonal. When only one firm advertises, the advertiser takes the whole market ($1,000); the non-advertiser gets $0. When both advertise, the campaigns cancel out and each earns $500. When neither advertises, both enjoy higher margins and earn $700.

Explanation (Advertise, Advertise) → QP = 500, PP = 500.
(QP Advertise, PP Not) → QP = 1000, PP = 0.
(QP Not, PP Advertise) → QP = 0, PP = 1000.
(Not, Not) → QP = 700, PP = 700.

Question 1b

If the two firms cooperate, which strategy pair maximizes joint profits, and what is that joint total?

Both Advertise — joint profit $1,000 Both Not Advertise — joint profit $1,400 One advertises, the other does not — joint profit $1,000 It doesn't matter — all four outcomes give the same joint profit

Hint Add the two payoffs in every cell. Pick the cell with the largest total.

Explanation Joint totals: (A,A) = 1,000; (A,N) and (N,A) = 1,000; (N,N) = 1,400. If the firms could enforce a deal, they would both refrain from advertising and split $1,400 in joint profit. Advertising money cancels out — it's a transfer to ad networks, not new surplus.

Question 1c

What is the dominant strategy for Quality Products?

Advertise Not Advertise No dominant strategy — best response depends on PP

Hint Compare QP's payoff across its two choices for each column (PP's move). A dominant strategy wins in every column.

Explanation If PP advertises: QP gets 500 (Advertise) vs 0 (Not) → Advertise wins.
If PP doesn't advertise: QP gets 1,000 (Advertise) vs 700 (Not) → Advertise wins.
Advertise is the dominant strategy for Quality Products — it beats Not Advertise in every column.

Question 1d

What is the dominant strategy for Perfection Performed?

Advertise Not Advertise No dominant strategy — best response depends on QP

Hint Because payoffs are symmetric, the same reasoning from 1c applies to PP — just compare rows instead of columns.

Explanation By symmetry: if QP advertises, PP earns 500 vs 0 → Advertise. If QP doesn't, PP earns 1,000 vs 700 → Advertise. Advertise is also dominant for Perfection Performed.

Question 1e

What is the predicted outcome of this game, and what is the resulting joint profit?

(Advertise, Advertise) — joint profit $1,000 (Not, Not) — joint profit $1,400 (Advertise, Not) — joint profit $1,000 No stable outcome — firms keep switching

Hint Both firms have the same dominant strategy. Put them together.

Explanation Both firms play their dominant strategy: Advertise. The Nash equilibrium is (Advertise, Advertise) with joint profit = 500 + 500 = $1,000. This is a classic prisoner's dilemma: acting in self-interest, each firm is worse off than if both had cooperated to refrain from advertising ($1,400 joint). The lost $400 is the cost of non-cooperation.

Part 2

Short Answer — Ricky Rock Star vs. Harry Hip Hop

Setup Two musicians — Ricky Rock Star (rock) and Harry Hip Hop (rap) — each decide whether to go it alone or collaborate.

Working alone, each captures his own genre → $5 M.
If both collaborate: each keeps their own $5 M market AND splits the new $3 M fusion audience evenly ($1.5 M each).
If one collaborates, the other goes alone: the solo artist releases first, grabs his own genre plus the fusion audience = $5 M + $3 M = $8 M. The collaborator gets $0 (too late to release).
If both go alone: the fusion audience gets disillusioned and buys nothing — each keeps his own $5 M, fusion = $0.

Question 2a — Complete the Payoff Matrix

Fill in each cell with the payoffs (in $ millions). Column = Ricky's choice, row = Harry's choice. For each cell, enter Harry's profit first, then Ricky's.

		Ricky Rock Star
		Alone	Collaborate
Harry Hip Hop	Alone	Harry $M Ricky $M	Harry $M Ricky $M
Harry Hip Hop	Collaborate	Harry $M Ricky $M	Harry $M Ricky $M

Hint Work one cell at a time. "Both Collaborate" means each gets his own $5M plus half of the $3M fusion. "One Alone, one Collaborate" means the solo artist scoops fusion ($8M) and the collaborator is stranded ($0).

Explanation (Harry Alone, Ricky Alone) → Harry 5, Ricky 5 (fusion dies).
(Harry Alone, Ricky Collaborate) → Harry 8, Ricky 0 (Harry releases first, grabs fusion).
(Harry Collaborate, Ricky Alone) → Harry 0, Ricky 8.
(Harry Collaborate, Ricky Collaborate) → Harry 6.5, Ricky 6.5 (each keeps own $5M + half of $3M fusion = $1.5M).

Question 2b

Does Ricky Rock Star have a strictly dominant strategy? If so, which one?

Yes — Alone dominates Collaborate Yes — Collaborate dominates Alone No — Ricky's best response depends on what Harry does

Hint Compare Ricky's two rows for each of Harry's choices. Does Alone beat Collaborate in both?

Explanation If Harry is Alone: Ricky earns 5 (Alone) vs 0 (Collaborate). Alone wins.
If Harry Collaborates: Ricky earns 8 (Alone) vs 6.5 (Collaborate). Alone wins again.
Alone strictly dominates Collaborate for Ricky.

Question 2c

Does Harry Hip Hop have a strictly dominant strategy? If so, which one?

Yes — Alone dominates Collaborate Yes — Collaborate dominates Alone No — Harry's best response depends on Ricky

Hint The game is symmetric — so whatever's true for Ricky is true for Harry.

Explanation By symmetry: if Ricky is Alone, Harry earns 5 (Alone) vs 0 (Collab) → Alone. If Ricky Collaborates, Harry earns 8 (Alone) vs 6.5 (Collab) → Alone. Alone strictly dominates Collaborate for Harry too.

Question 2d

What will be the outcome of this game?

(Alone, Alone) — each earns $5M; fusion dies (Collaborate, Collaborate) — each earns $6.5M (Alone, Collaborate) — Harry wins, Ricky stranded Unpredictable — no stable outcome

Hint Put both dominant strategies together. What's the intersection?

Explanation Both players play their dominant strategy Alone. The Nash equilibrium is (Alone, Alone): each earns $5M, fusion audience gets nothing. No one has an incentive to deviate — if Ricky switched to Collaborate while Harry stays Alone, Ricky would drop from $5M to $0.

Question 2e

Is this outcome socially optimal? If not, which outcome is — and why?

Yes — no one can be made better off without hurting the other No — (Collaborate, Collaborate) is socially optimal: both move from $5M to $6.5M No — (Alone, Collaborate) maximizes total $M There is no way to tell without more information

Hint Compare (Alone, Alone) at (5, 5) to (Collaborate, Collaborate) at (6.5, 6.5). Can you move from one to the other making both better off?

Explanation Not socially optimal. Moving from (Alone, Alone) at ($5M, $5M) to (Collaborate, Collaborate) at ($6.5M, $6.5M) makes both musicians better off — total surplus rises from $10M to $13M, and the fusion audience finally gets served. This is the classic prisoner's dilemma: individually rational choices produce a collectively bad outcome. Without a binding contract, each musician fears being stranded at $0 and defects to Alone.

Part 3

Multiple Choice

Figure 17-1 — Duopoly Market Two firms serve this market and each faces the same horizontal marginal cost curve. The MR curve shown is the one a monopolist would face. Use this figure for MC 1 and MC 2.

Question MC 1 — Refer to Figure 17-1

If the two firms collude successfully,

the total output will be 2 units and the price will be $6.00 per unit. the total output will be 2 units and the price will be $8.00 per unit. the total output will be 4 units and the price will be $6.00 per unit. there will be no deadweight loss.

Hint Successful collusion = act like a single monopolist. Use MR = MC to find Q, then read the price up from that Q to the demand curve (not MR).

Explanation Colluding firms mimic a monopoly. Demand: P = 10 − Q, so MR = 10 − 2Q. Set MR = MC: 10 − 2Q = 6 → Q = 2. Price from demand: P = 10 − 2 = $8. Answer: B.

Question MC 2 — Refer to Figure 17-1

With zero fixed cost, if collusion succeeds, each firm earns a profit of

$8.00 $2.00 $4.00 $16.00

Hint Compute total profit first: TR − TC at Q = 2, P = $8, MC = $6. Then split between the two firms.

Explanation TR = P × Q = $8 × 2 = $16. TC = MC × Q (zero fixed cost) = $6 × 2 = $12. Total profit = $16 − $12 = $4. Split evenly = $2 per firm. Answer: B.

Table 17-6 — HomeMax vs. Lopes Two home-improvement stores, Lopes and HomeMax, each decide whether to expand their store and parking lot. Cells show increases in annual profit (in $ millions). Columns = Lopes's choice, rows = HomeMax's choice. Use this for MC 3 – MC 6.

		Lopes
		Expand	Do Not Expand
HomeMax	Expand	Lopes = 1.0 HomeMax = 1.5	Lopes = 0.4 HomeMax = 3.4
HomeMax	Do Not Expand	Lopes = 3.2 HomeMax = 0.6	Lopes = 2.0 HomeMax = 2.5

Question MC 3 — Refer to Table 17-6

Pursuing its own best interest, Lopes will

expand only if HomeMax also expands. expand only if HomeMax does not expand. expand regardless of the decision made by HomeMax. not expand regardless of the decision made by HomeMax.

Hint Compare Lopes's two Expand/Not payoffs for each row of HomeMax's choice.

Explanation If HomeMax expands: Lopes gets 1.0 (Expand) vs 0.4 (Not). Expand wins.
If HomeMax doesn't: Lopes gets 3.2 (Expand) vs 2.0 (Not). Expand wins.
Expand regardless → Answer: C.

Question MC 4 — Refer to Table 17-6

Pursuing its own best interest, HomeMax will

expand only if Lopes also expands. expand only if Lopes does not expand. expand regardless of the decision made by Lopes. not expand regardless of the decision made by Lopes.

Hint Compare HomeMax's two payoffs for each of Lopes's column choices.

Explanation If Lopes expands: HomeMax gets 1.5 (Expand) vs 0.6 (Not). Expand.
If Lopes doesn't: HomeMax gets 3.4 (Expand) vs 2.5 (Not). Expand.
Expand regardless → Answer: C.

Question MC 5 — Refer to Table 17-6

If both stores follow a dominant strategy, Lopes's annual profit will grow by

$0.4 million $1.0 million $2.0 million $3.2 million

Hint From MC 3 and MC 4, both firms expand. Find Lopes's payoff in that (Expand, Expand) cell.

Explanation Dominant strategy for both = Expand. In the (Expand, Expand) cell, Lopes = $1.0 million. Answer: B.

Question MC 6 — Refer to Table 17-6

When this game reaches a Nash equilibrium, annual profit will grow by

$1.5 million for HomeMax and $1.0 million for Lopes. $3.4 million for HomeMax and $0.4 million for Lopes. $0.6 million for HomeMax and $3.2 million for Lopes. $2.5 million for HomeMax and $2.0 million for Lopes.

Hint In a Nash equilibrium, neither player wants to deviate. Both dominant strategies point to the same cell.

Explanation Both firms play their dominant strategy Expand. The Nash equilibrium is (Expand, Expand): HomeMax = $1.5M, Lopes = $1.0M. Answer: A. (Note: this is also a prisoner's dilemma — both would prefer the (Not Expand, Not Expand) cell at (2.5, 2.0).)

Question MC 7

Which of the following examples illustrates an oligopoly market?

A farmers' market with many individuals selling sweet corn and tomatoes. A city whose electrical service is provided by one electric co-operative. A city with two firms licensed to sell school uniforms for the local schools. A city with many independently owned hair salons.

Hint Oligopoly = a few firms with strategic interaction. "Many" means competition or monopolistic competition; "one" means monopoly.

Explanation C. Two licensed firms = a duopoly, which is a type of oligopoly. A = perfect competition (many sellers, homogeneous product). B = monopoly (one seller). D = monopolistic competition (many sellers, differentiated service).

Question MC 8

As the number of competing firms in an oligopoly grows very large, the market outcome

approaches the monopoly outcome. approaches the perfectly competitive outcome (P ≈ MC). becomes indeterminate — there is no stable equilibrium. produces greater deadweight loss than a monopoly would.

Hint More firms → each firm's market power shrinks → harder to collude → behavior looks more like what kind of market?

Explanation Mankiw's key result: as oligopoly size N → ∞, the Nash equilibrium output approaches the competitive level and price approaches MC. The output effect (P > MC gives each firm an incentive to expand) dominates the price effect as each firm's share shrinks. With many firms, collusion is impossible and outcomes converge to perfect competition.

Part 4

True or False

Question TF 8

Game theory is just as necessary for understanding competitive or monopoly markets as it is for understanding oligopolistic markets.

Hint Game theory is about strategic interaction — when one firm's best move depends on what rivals do. When does that apply?

Explanation False. In perfect competition (price takers) and monopoly (no rivals), a firm's best action does not depend on any specific competitor's move. Game theory is especially necessary for oligopoly because it's the only structure where strategic interaction drives behavior.

Question TF 9

In a competitive market, strategic interactions among the firms are not important.

Hint A competitive firm is a price taker. Does it care what any one other firm does?

Explanation True. Each competitive firm is a price taker, too small to affect the market price. It doesn't try to outmaneuver a specific rival — it just sells at the going price. Strategic interaction matters only when firms are few enough to influence each other.

Question TF 10

Oligopolies produce more when they collude than when they do not.

Hint A successful cartel acts like a monopoly. What does a monopoly do with output relative to competition?

Explanation False. Collusion means joint monopoly: restrict output to push the price up. Oligopolies produce less when they collude than when they compete — that's why cartels are so tempting for firms (and so bad for consumers). In Figure 17-1, collusion gives Q = 2 while individual competition would give Q = 4.

Question TF 11

A dominant strategy is a strategy that is best for a player in a game regardless of the strategies chosen by the other players.

Hint This is literally the textbook definition.

Explanation True. That's exactly the definition: a dominant strategy gives you the highest payoff no matter what the opponent does. In both Q1 (Advertise) and Q2 (Alone), each player has such a strategy — which makes the Nash equilibrium easy to predict.

Question TF 12

Every Nash equilibrium must involve a dominant strategy for at least one player.

Hint A Nash equilibrium just requires that no one wants to unilaterally deviate — it doesn't require dominance.

Explanation False. A Nash equilibrium only requires that each player's choice is a best response to what the others are doing. Dominant strategies are a special case. Many games (coordination games, battle of the sexes) have Nash equilibria without any dominant strategy. Dominance implies Nash, but Nash does not imply dominance.

Part 5

Short Answer — Concept Checks

Question SA 1

In a one-shot prisoner's dilemma, both players defect. How can repeated play between the same two players change this outcome — and why?

It can't — a Nash equilibrium in the stage game is a Nash equilibrium forever. Repeated interaction lets each player punish defection in future rounds, so cooperation can be sustained as a long-run equilibrium. Repeated play makes players care less about payoffs, so they cooperate out of habit. Repeated play converts the game into perfect competition, so dominant strategies disappear.

Hint In a one-shot game, there's no future. In a repeated game, future rounds give each player a way to respond to the other's current behavior.

Explanation B. With repeated play, each firm can adopt a trigger strategy: "I'll cooperate as long as you do, but if you ever defect, I'll defect forever after." The threat of lost future profits (the punishment phase) can outweigh the short-run gain from defecting today. This is how real-world cartels (OPEC, airline capacity) sometimes sustain collusion even though each member has a short-run incentive to cheat.

Question SA 2

Cartels like OPEC formally agree to restrict output, yet member nations frequently cheat and produce more than their quotas. Using the logic of the prisoner's dilemma, explain why collusion is inherently unstable.

At the collusive price, P > MC, so each firm has a unilateral incentive to secretly expand output. Cheating is the one-shot dominant strategy. Antitrust authorities force firms to defect; without regulation, collusion would be stable. Cartel agreements are always written poorly, so members misunderstand their quotas. Adding more firms makes the cartel more efficient, which paradoxically undermines profits.

Hint At the cartel price, any individual firm can increase its own profit by selling one more unit (since P > MC). What does this mean for the cartel's stability?

Explanation A. The collusive outcome pegs P at the monopoly level, well above MC. Any individual member can earn extra profit by cheating — sneaking one more unit onto the market at P > MC brings positive marginal profit. Because every member faces the same temptation, "cheat" is the dominant strategy in the stage game. Cartels hold together only when (i) cheating can be detected and (ii) punishment (price wars, lost future profits) is credible enough to outweigh the gains from defection.

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