Oligopoly and Game Theory — AP Microeconomics Study Guide

For: AP Microeconomics candidates sitting AP Microeconomics.

Covers: concentration ratios, Herfindahl-Hirschman Index (HHI), dominant strategy, Nash equilibrium, prisoner’s dilemma, collusive oligopoly, cartels, payoff matrix analysis, and sequential game entry deterrence for AP Microeconomics Unit 4 Imperfect Competition.

You should already know: The profit maximization rule MR = MC for all firms. How market concentration relates to market power. The difference between perfect competition and monopoly outcomes.

A note on the practice questions: All worked questions in the "Practice Questions" section below are original problems written by us in the AP Microeconomics style for educational use. They are not reproductions of past College Board / Cambridge / IB papers and may differ in wording, numerical values, or context. Use them to practise the technique; cross-check with official mark schemes for grading conventions.

1. What Is Oligopoly and Game Theory?

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.

According to the AP Microeconomics Course and Exam Description (CED), oligopoly and game theory make up approximately 4% of the total exam score, and questions appear in both multiple-choice (MCQ) and free-response (FRQ) sections. Common notation conventions used on the exam are: market shares are percentages ranging from 0 to 100 for concentration calculations, and payoff matrices list the row player’s payoff first, followed by the column player’s payoff. Oligopoly is often referred to as a concentrated industry in industry regulation contexts, a common synonym on exam questions.

2. Measuring Market Concentration

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 n-firm concentration ratio (most commonly the 4-firm concentration ratio, CR4) and the Herfindahl-Hirschman Index (HHI).

The 4-firm concentration ratio is the sum of the market shares (in percentage points) of the four largest firms in the market: $$C{R}_4=s_1+s_2+s_3+s_4$$ CR4 ranges from 0 (many tiny firms, perfect competition) to 100 (the top four firms control the entire market). 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.

HHI addresses this limitation by squaring each firm’s market share before summing, which gives more weight to larger firms: $$\text{HHI}=\sum _{i=1}^n{s}_i^2$$ where $s_i$ is the market share of firm $i$ in percentage points. HHI ranges from near 0 (perfect competition) to 10,000 (pure monopoly, one firm with 100% share: $100^2=10000$). The standard threshold used on the AP exam 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. The 4-firm concentration ratio sums the market shares of the four largest firms. The top four are 35%, 30%, 20%, 10%.
2. Calculate CR4: $35+30+20+10=95\%$.
3. Calculate HHI by squaring each firm’s market share and summing: $35^2+30^2+20^2+10^2+5^2=1225+900+400+100+25=2650$.
4. The AP standard threshold for high concentration is HHI > 2500. Since 2650 > 2500, this 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

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. The most common representation for simultaneous-move games (both players choose at the same time) is a payoff matrix.

Two core concepts tested on every AP exam are dominant strategy and Nash equilibrium:

• A dominant strategy is 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 outcome where both play their dominant strategy is a dominant strategy equilibrium.
• A Nash equilibrium is 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 easiest method to find these is the "best response" method: for each of the opponent’s possible choices, circle the highest payoff for your player. If one strategy is circled for all opponent choices, it is dominant. Any cell where both payoffs are circled is a Nash equilibrium.

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 are (A’s daily profit, B’s daily profit):

1. Find A’s best responses: If B parks downtown, A earns $120downtownvs$180 at the beach, so best response is beach. If B parks at the beach, A earns $200downtownvs$100 at the beach, so best response is downtown. A has no dominant strategy, because A’s best choice depends on B’s choice.
2. Find B’s best responses: If A parks downtown, B earns $80downtownvs$150 at the beach, so best response is beach. If A parks at the beach, B earns $160downtownvs$90 at the beach, so best response is downtown. B also has no dominant strategy.
3. Check for cells where both are best responses: The cell (A: Downtown, B: Beach) has both payoffs circled (A’s best response to B beach is downtown, B’s best response to A downtown is beach). The cell (A: Beach, B: Downtown) also has both payoffs circled.
4. There are two Nash equilibria: (A downtown, B beach) and (A beach, B downtown).

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 the Prisoner's Dilemma

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, which is also common. Collusion is illegal in most developed countries, but it still occurs, and its instability is a core topic on the AP exam.

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 with the agreement. 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 and over), strategies like tit-for-tat (cooperate if the opponent cooperated, punish cheating by matching it in the next round) can sustain collusion over time.

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):

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, $15M(cheat)>$12M (comply); if ConstructInc cheats, $7M(cheat)>$4M (comply). Cheating is a dominant strategy for BuildCo. The same logic applies to ConstructInc: cheating is also a dominant strategy.
3. The equilibrium is both firms cheat, earning $7 million each.
4. This is a prisoner’s dilemma because the equilibrium outcome (both cheat, $7Meach)isworsefor\ast both\ast firmsthanthecooperativeoutcome(bothcomply,$12M each). The individual incentive to cheating prevents 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

So far we have covered simultaneous-move games, where both players choose at the same time. 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 $5millionfromenteringvs$0 from staying out. $5 > 0, so Beta will enter.
3. If Alpha sets a low price: Beta earns -$2millionfromenteringvs$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 $20million(afterentry);ifAlphachooseslowprice,Alphaearns$25 million (after Beta stays out). $25 > 20, so Alpha chooses low price.
5. The equilibrium outcome is Alpha sets a low limit price, Beta stays out, with payoffs ($25million,$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 (and how to avoid them)

• 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. Practice Questions (AP Microeconomics Style)

Question 1 (Multiple Choice)

The market for wireless headphones has three firms with market shares of 45%, 35%, and 20%. What is the Herfindahl-Hirschman Index (HHI) for this market? A) 100 B) 1100 C) 3650 D) 10000

Worked Solution: To calculate HHI, we square the percentage market share of each firm and sum the results. Calculate each term: $45^2=2025$, $35^2=1225$, $20^2=400$. Sum: $2025+1225+400=3650$. The options trap students who forget to square market shares or use unscaled decimal values. The correct answer is C.

Question 2 (Free Response)

Two soft drink companies, ColaCo and PopCorp, compete in a small national market. Both can choose to spend $10milliononadvertising,or$0 on advertising. Payoffs (annual profit in millions of USD, after advertising costs) are (ColaCo profit, PopCorp profit):

(a) Identify any dominant strategies for ColaCo and PopCorp. (b) Find the Nash equilibrium, and explain why this outcome is a prisoner’s dilemma. (c) How would the outcome change if this game is repeated indefinitely?

Worked Solution: (a) For ColaCo: If PopCorp spends $10Monads,ColaCoearns15from$10M vs 5 from $0,so15>5.IfPopCorpspends$0, ColaCo earns 30 from $10Mvs25from$0, so 30>25. Spending $10MonadvertisingisadominantstrategyforColaCo.Byidenticallogic,$10M advertising is also a dominant strategy for PopCorp. (b) The Nash equilibrium is both firms spend $10Monadvertising,earning$15 million each. This is a prisoner’s dilemma because both firms would be better off if both spent $0(earning$25 million each), but the individual incentive to advertise leads both to the lower-profit equilibrium. (c) In an indefinitely repeated game, a tit-for-tat strategy can sustain the cooperative outcome (both spend $0 on advertising). Each firm cooperates as long as the other firm cooperated in the previous round, and punishes cheating by advertising if the other firm cheated. The long-term cost of punishment outweighs the short-term gain from cheating, so cooperation is sustained.

Question 3 (Application / Real-World Style)

Regulators are reviewing a merger between two regional bank chains. The market currently has 8 banks: two with 30% market share each, and six smaller banks with 3.33% market share each (total = 30 + 30 + 6*(3.33) ≈ 100%). The two large banks propose merging. Per regulatory rules, a merger is flagged for further review if post-merger HHI is above 2500 and the HHI increases by more than 100 points. Will this merger be flagged?

Worked Solution: Calculate pre-merger HHI first: $30^2+30^2+6\ast (3.33^2)\approx 900+900+6\ast (11.11)\approx 1800+66.66\approx \mathrm{1866.66.}Post-merger,thecombinedbankhas30+30=60$60^2 + 6*(3.33^2) ≈ 3600 + 66.66 ≈ 3666.66. The change in HHI is 3666.66 - 1866.66 = 1800. Post-merger HHI is 3666.66 > 2500, and the increase is 1800 > 100. This merger will be flagged for further regulatory review, as it creates a highly concentrated market with a large increase in market power for the merged firm.

8. Quick Reference Cheatsheet

9. What's Next

Oligopoly and game theory is the capstone of Unit 4 Imperfect Competition, building on your understanding of monopoly and monopolistic competition to model interdependent firm decision making. Next in the AP Micro syllabus you will apply the tools from this chapter to antitrust policy and regulatory analysis of concentrated markets, which requires fluent mastery of HHI calculation, Nash equilibrium, and dominant strategy identification. Without mastering the core concepts in this chapter, you will struggle to score full points on multi-part FRQs that ask you to evaluate the effects of mergers or collusive behavior. This topic also reinforces the core course theme of how market power impacts economic efficiency, which appears across all market structure units.

Antitrust Policy Monopolistic Competition Public Policy Toward Market Power