Oligopoly and Game Theory

AP Microeconomics· AP Microeconomics CED — Imperfect Competition· 14 min read

1. Core Definition of Oligopoly★★☆☆☆⏱ 2 min

Oligopoly is a market structure defined by a small number of large, strategically interdependent firms, protected by high barriers to entry that block new competitors from entering the market. Unlike perfect competition (where firms are price takers) or monopoly (where there is only one firm), oligopolistic firms must account for the actions of their rivals when setting price, output, advertising, or other strategic choices. Game theory is the formal framework economists use to model this interdependent decision making, predicting the outcomes firms will choose and comparing them to socially optimal outcomes.

Oligopoly and game theory make up approximately 4% of the total AP Microeconomics exam score, and questions appear in both multiple-choice (MCQ) and free-response (FRQ) sections. A standard convention on the exam is that payoff matrices list the row player’s payoff first, followed by the column player’s payoff.

2. Measuring Market Concentration★★☆☆☆⏱ 3 min

To classify markets as oligopolistic, economists first measure how much market share is controlled by the largest firms. Two standard measures tested on the AP exam are the 4-firm concentration ratio (CR4) and the Herfindahl-Hirschman Index (HHI).

📘 Definition

4-Firm Concentration Ratio

CR_4

The sum of the percentage market shares of the four largest firms in a market

Example:

Ranges from 0 (perfect competition) to 100 (top four firms control the entire market)

CR_4 = s_1 + s_2 + s_3 + s_4

The main limitation of CR4 is that it does not distinguish between a market with one very large firm and three small ones, versus a market with four equal large firms, even though these two markets have very different levels of market power.

📘 Definition

Herfindahl-Hirschman Index

HHI

Sum of the squared percentage market shares of all firms in a market, giving extra weight to larger firms to address CR4's limitation

Example:

A pure monopoly has HHI = $10 0^{2} = 10000$

\text{HHI} = \sum_{i=1}^n s_i^2

The standard AP exam threshold is that HHI above 2500 indicates a highly concentrated (oligopolistic) market.

📐 Worked Example

Suppose the craft beer market in a state has 5 firms with market shares: 35%, 30%, 20%, 10%, 5%. Calculate (i) the 4-firm concentration ratio, (ii) the HHI, and (iii) state if the market is highly concentrated.

1
Identify the four largest firms and sum their market shares:
2
$35 + 30 + 20 + 10 = 95$
3
Calculate HHI by squaring each firm's market share and summing:
4
$35^2 + 30^2 + 20^2 + 10^2 + 5^2 = 1225 + 900 + 400 + 100 + 25 = 2650$
5
Compare to the AP threshold: 2650 > 2500, so the market is highly concentrated.

Exam tip:

If market shares are given as decimals (e.g. 0.35 instead of 35), multiply the sum of squared decimals by 10,000 to get the standard percentage-based HHI that matches AP exam thresholds.

3. Dominant Strategy and Nash Equilibrium★★★☆☆⏱ 4 min

Game theory models strategic interactions between players (oligopoly firms) who choose strategies (e.g. set high price, advertise heavily) and receive payoffs (usually profit) based on the combination of all players' choices. Simultaneous-move games, where both players choose at the same time, are most often represented by a payoff matrix.

📘 Definition

Dominant Strategy

A strategy that gives a player a higher payoff than any other strategy, no matter what strategy the other player chooses. If both players have a dominant strategy, the resulting outcome is a dominant strategy equilibrium.

📘 Definition

Nash Equilibrium

A set of strategies where no player can improve their own payoff by changing their strategy, given the strategy the other player is playing. Every dominant strategy equilibrium is a Nash equilibrium, but not all Nash equilibria have dominant strategies.

The best response method is the easiest approach to find these outcomes: for each of the opponent's possible choices, mark the highest payoff for your player. If one strategy is marked for all opponent choices, it is dominant. Any cell where both payoffs are marked is a Nash equilibrium.

	B: Downtown	B: Beach
A: Downtown	( $120,$ 80)	( $200,$ 150)
A: Beach	( $180,$ 160)	( $100,$ 90)

📐 Worked Example

Two food trucks, Taco Truck A (row player) and Taco Truck B (column player), choose to park either downtown or at the beach. Payoffs show A's daily profit first, then B's. Does either player have a dominant strategy? What is the Nash equilibrium?

1
Find A's best responses: If B parks downtown, A earns $120 d o w n t o w n v s$ 180 at the beach → best response is beach. If B parks at the beach, A earns $200 d o w n t o w n v s$ 100 at the beach → best response is downtown.
2
A has no dominant strategy, because A's best choice depends entirely on B's choice.
3
Find B's best responses: If A parks downtown, B earns $80 d o w n t o w n v s$ 150 at the beach → best response is beach. If A parks at the beach, B earns $160 d o w n t o w n v s$ 90 at the beach → best response is downtown.
4
B also has no dominant strategy.
5
Check for cells where both payoffs are best responses: both (A Downtown, B Beach) and (A Beach, B Downtown) meet this condition.
6
Final result: there are two separate Nash equilibria.

Exam tip:

Always explicitly mark best responses in your FRQ working. AP graders award partial credit for correct best response calculations even if you get the final equilibrium wrong, as long as your method is correct.

4. Collusion, Cartels, and Prisoner's Dilemma★★★☆☆⏱ 3 min

Collusion is an agreement between oligopoly firms to restrict output and raise price, acting like a single monopolist to maximize total industry profit, then split the profits between members. A formal collusive agreement is called a cartel; tacit collusion is an informal unwritten agreement to coordinate prices. Collusion is illegal in most developed countries, and its inherent instability is a core AP exam topic.

The prisoner's dilemma is a classic game that explains why cartels are almost always unstable. In a prisoner's dilemma, both firms have a dominant strategy to cheat on the collusive agreement (by cutting price or increasing output to capture more market share), leading to an equilibrium where both firms earn lower profit than they would if they both complied. The individual incentive to cheat overwhelms the collective benefit of cooperation, so cartels break down unless they have a way to punish cheating. In repeated games where firms interact over time, strategies like tit-for-tat can sustain collusion over time.

	ConstructInc: Comply	ConstructInc: Cheat
BuildCo: Comply	( $12,$ 12)	( $4,$ 15)
BuildCo: Cheat	( $15,$ 4)	( $7,$ 7)

📐 Worked Example

Two construction companies, BuildCo and ConstructInc, collude to split contracts in a local market. Both can either comply with the agreement (turn down extra contracts to keep prices high) or cheat (accept extra contracts to undercut the other firm). Payoffs are (BuildCo annual profit, ConstructInc annual profit, in millions of dollars). What is the collusive outcome, what is the equilibrium, and why is this a prisoner's dilemma?

1
The collusive (cooperative) outcome is both firms comply, so each earns $12 million, which is higher than the equilibrium profit for both.
2
Check for dominant strategies: For BuildCo, if ConstructInc complies: $15 M (c h e a t) >$ 12M (comply); if ConstructInc cheats: $7 M (c h e a t) >$ 4M (comply). Cheating is a dominant strategy for BuildCo.
3
By identical logic, cheating is also a dominant strategy for ConstructInc.
4
The equilibrium outcome is both firms cheat, earning $7 million each.
5
This is a prisoner's dilemma because the equilibrium outcome (both cheat, $7 M e a c h) i s w or se f or b o t h f i r m s t han t h ecoo p er a t i v eo u t co m e (b o t h co m pl y,$ 12M each). Individual incentives prevent them from reaching the mutually better outcome.

Exam tip:

When asked why cartels are unstable, always explicitly mention the individual incentive to cheat on the collusive agreement. This is the core point AP graders look for, not just a generic statement that 'cartels break down.'

5. Sequential Games and Entry Deterrence★★★★☆⏱ 3 min

Sequential games are games where one player moves first, then the second player observes the first move and chooses their own strategy. A common application in oligopoly is entry deterrence, where an incumbent firm (existing in the market) moves first, and a potential entrant decides whether to enter the market after observing the incumbent’s choice.

To solve sequential games, we use backward induction: start from the last mover’s choice, find their optimal decision for every possible first move, then work back to the first mover, who chooses their strategy to maximize their own payoff given the anticipated response of the second mover.

📐 Worked Example

An incumbent cable provider (Alpha, first mover) can set either a high monopoly price or a low limit price to deter entry. A potential new entrant (Beta, second mover) observes Alpha’s price, then decides to enter or stay out. Payoffs are (Alpha annual profit, Beta annual profit, in $ millions): If Alpha sets high price: Beta enters → (20, 5); Beta stays out → (40, 0). If Alpha sets low price: Beta enters → (5, -2); Beta stays out → (25, 0). What is the equilibrium outcome?

1
Start with the second mover (Beta) and find Beta's optimal choice for each of Alpha's moves.
2
If Alpha sets a high price: Beta earns $5 mi l l i o n f r o m e n t er in g v s$ 0 from staying out. $5 > 0, so Beta will enter.
3
If Alpha sets a low price: Beta earns - $2 mi l l i o n f r o m e n t er in g v s$ 0 from staying out. $0 > -2, so Beta will stay out.
4
Work back to Alpha's choice. Alpha knows Beta's response: if Alpha chooses high price, Alpha earns $20 mi l l i o na f t er e n t r y; i f A l p ha c h ooses l o w p r i ce, A l p ha e a r n s$ 25 million after Beta stays out. $25 > 20, so Alpha chooses low price.
5
Final equilibrium: Alpha sets a low limit price, Beta stays out, with payoffs ( $25 mi l l i o n,$ 0).

Exam tip:

Never solve sequential games starting from the first mover. Working forward ignores the first mover's ability to anticipate the second mover's response, which almost always leads to an incorrect equilibrium. Always use backward induction.

6. Common Pitfalls

Wrong move:

Mixing up the order of payoffs in a payoff matrix, taking the column player’s payoff as the row player’s.

Why:

Students forget the standard convention that the row player’s payoff comes first, and scan the matrix left to right without checking.

Correct move:

Before starting any analysis, label the matrix clearly: confirm which player is row, which is column, and note 'row payoff first' to avoid misreading.

Wrong move:

Claiming that all Nash equilibria must have a dominant strategy for both players.

Why:

Students confuse the special case of dominant strategy equilibrium with the general definition of Nash equilibrium.

Correct move:

Remember that games without dominant strategies can still have one or more Nash equilibria. Always check for best responses even if no dominant strategy exists.

Wrong move:

Calculating HHI as the sum of squared decimal market shares without scaling, getting a value like 0.285 instead of 2850.

Why:

Some textbooks teach HHI as a decimal between 0 and 1, but AP always uses the percentage-based HHI between 0 and 10,000.

Correct move:

If market shares are given as decimals, multiply the sum of squares by 10,000 to convert to the standard AP form.

Wrong move:

Claiming the prisoner’s dilemma outcome is inefficient for society because it is bad for firms.

Why:

Students confuse inefficiency for firms with inefficiency for society.

Correct move:

For price competition, the prisoner’s dilemma outcome (both cheat, lower prices) is more efficient for society than the collusive outcome, even though it is worse for firms. Always clarify who gains and loses when discussing efficiency.

Wrong move:

Saying that the Nash equilibrium is the best possible outcome for both players.

Why:

Students associate equilibrium with 'optimal' and forget the prisoner’s dilemma example where both are worse off at equilibrium.

Correct move:

Remember Nash equilibrium only means no player can unilaterally improve their own outcome, given the other player’s choice. It does not mean the outcome is socially or jointly optimal.

7. Quick Reference Cheatsheet

Concept	Key Rule	AP Thumbnail
CR4	Sum of top 4 % market shares	Ranges 0-100, ignores firm size distribution
HHI	Sum of squared % market shares	HHI > 2500 = highly concentrated (oligopoly), ranges 0-10000
Dominant Strategy	Best choice regardless of opponent	If both have dominant strategy, outcome is equilibrium
Nash Equilibrium	No unilaterally better move	Can have multiple equilibria; no dominant strategy required
Prisoner's Dilemma	Equilibrium < cooperative outcome for both	Core explanation for cartel instability
Sequential Games	Solve via backward induction	Start at last mover, work back to first mover

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2023 · MCQ
HHI calculation for 3-firm market
2022 · FRQ
Prisoner's dilemma game analysis

Going deeper

unit overviewAP Microeconomics Unit 4 Imperfect Competition OverviewParent unit content

What's Next

After mastering oligopoly and game theory, you have completed the core market structure topics in AP Microeconomics Unit 4. This framework of strategic interdependence is foundational for understanding firm behavior in most real-world markets, and appears regularly in both multiple-choice and free-response questions on the AP exam. Understanding cartel instability and entry deterrence also connects directly to regulatory policy topics covered later in the course. You can now review related imperfect competition topics, reinforce your learning with practice questions, or return to the unit overview for additional review.