Oligopoly and Game Theory: Payoff Matrices and Why Cartels Cheat

Objectives

• Students will be able to explain mutual interdependence as the defining feature of oligopoly and contrast it with the price-taking behavior of perfect competition.
• Students will be able to identify each player's dominant strategy in a two-firm payoff matrix by holding the rival's choice fixed and comparing best responses.
• Students will be able to locate the Nash equilibrium of a payoff matrix and explain why it can differ from the jointly optimal (collusive) outcome.
• Students will be able to explain why cartels are unstable using the prisoner's dilemma incentive to cheat.

Materials (all free, no student accounts needed)

• Oligopoly module lesson
• Monopoly sandbox graph
• Oligopoly practice questions
• Unit 4.5 topic page

Five-minute warm-up, no prep

Open one of these on the projector. Students say what they think happens to price and quantity before anything moves, lock it in, and then the graph plays out step by step. No accounts, nothing graded or stored.

• Tea Gets Pricier
• Coffee Beans Get Expensive
• Printers Get Pricier, Ink Suffers

Warm-up (10 min)

• Project this on the board without comment: 'Verizon, AT&T, and T-Mobile all charge about the same for unlimited data, year after year.' Ask students to write one sentence explaining why three rivals would land on nearly identical prices.
• Think-pair-share for 3 minutes, then cold-call three students. Steer answers toward the idea that each firm watches the other two before it moves. Do not define oligopoly yet; let the tension sit.

Direct instruction (34 min)

• Define oligopoly: a small number of large firms whose profits depend on rivals' choices. Name the trait AP readers want: mutual interdependence. Contrast with perfect competition (price taker, ignores rivals) and monopoly (no rivals to watch).
• Build a payoff matrix live using the Samsung/Apple advertising example from the module (payoffs in millions, Samsung listed first: both big ads = 5,5; Samsung big/Apple small = 9,2; Samsung small/Apple big = 2,9; both small = 7,7).
• Walk the dominant-strategy test out loud: hold Apple's choice fixed, ask what Samsung should do; repeat for the other column. Do the same for Apple. Land on both-big-ads as the Nash equilibrium.
• Make the punchline explicit: both firms would earn 7 each if they colluded on small ads, but each has a private incentive to defect to 9. That gap is the prisoner's dilemma and the reason cartels break down.
• Add the vocabulary AP tests: collusion, cartel, and why open collusion is illegal, then note the kinked demand curve only as a why-prices-stay-sticky story, not a required graph.

Guided practice (32 min)

• Project /sandbox/monopoly. Tell students a cartel that colludes perfectly acts like one monopolist splitting the profit, so the monopoly graph is the cartel's target.
• Have a student drag the marginal cost curve to a new level and read off the profit-maximizing quantity where MR = MC and the price up on the demand curve. Write that (quantity, price) on the board as 'the cartel deal.'
• Cold-call: 'At that agreed price, if one firm secretly sells ten more units, does its revenue on those units exceed its marginal cost?' Elicit yes, that is the temptation to cheat that the matrix predicts.
• Return to the payoff matrix and have partners fill in a blank 2x2 for two gas stations choosing High Price or Low Price (you supply four payoff pairs). Circulate; make each pair circle the dominant strategy and box the Nash cell.
• Cold-call two pairs to defend their Nash cell using the best-response logic, not intuition.

Independent practice (19 min)

• Assign 6 to 8 items from /practice/oligopoly, prioritizing the matrix-reading and dominant-strategy questions.
• Students who finish early write a two-sentence answer to: 'A payoff matrix has no dominant strategy for either player. How would you still find the Nash equilibrium?'

Exit ticket

• Give a fresh 2x2 payoff matrix (numbers only). Students state each firm's dominant strategy if one exists and mark the Nash equilibrium cell.
• Grade for 2 points: 1 for correctly applying the best-response test to at least one player, 1 for the correct Nash cell.
• Any student who picks the jointly best cell instead of the Nash cell has the exact misconception to reteach the next day.

Homework

• Read the Cartels and Collusion section of /micro/oligopoly and write a short paragraph explaining, in OPEC terms, why a member country has an incentive to exceed its production quota.
• Finish any remaining /practice/oligopoly questions started in class.

Differentiation

• For students who struggle with matrices, give a pre-highlighted grid where the rival's fixed column is shaded, so the comparison is one column at a time.
• Stretch: hand advanced students a 2x2 with two Nash equilibria (a coordination game) and ask them to explain why dominant-strategy reasoning fails there.
• For English learners, provide the best-response test as a three-step checklist taped to the desk: cover a column, compare the two payoffs, circle the bigger.

Misconceptions to head off

• Wrong: the Nash equilibrium is always the cell where total profit is highest. Correction: Nash is where neither firm can gain by switching alone; it is often worse for both than the collusive cell.
• Wrong: a firm compares its own two payoffs down a column to the rival's payoffs. Correction: a player only compares its OWN payoffs while holding the rival's choice fixed.
• Wrong: cartels are stable because collusion is profitable. Correction: the same self-interest that makes collusion tempting makes every member want to cheat, so cartels tend to collapse.
• Wrong: oligopoly means firms sell identical products. Correction: oligopolists can sell identical (steel) or differentiated (cars) goods; the defining trait is interdependence, not the product.