Cartels and cheating
Learning goals
After this page, you can:
- Explain why rivals want to coordinate, and compute each member’s share from a cartel price and quota.
- Show with numbers why each member is tempted to cheat, and why a cut that rivals copy pays only once.
- Name the conditions that make coordination easier, and tell apart an explicit agreement (illegal) from rivals who simply watch and match posted prices.
The idea
Two gas stations face each other at a highway exit. Both owners know a simple fact. If they both posted $5.10 instead of fighting, each would earn more. Neither has to say a word. Each can read the other’s sign from across the road. And each also knows something else: the day it drops its price by a dime, the other will see it before lunch.
A market with only a few sellers, where each one watches the others, is an oligopoly. This page is about the strongest temptation in an oligopoly: to stop competing.
Why rivals want a deal. A single owner of both stations would not fight itself. It would pick the total volume that makes the most money for the whole exit, and charge the price that sells exactly that volume. That is the monopoly plan from Week 5. A cartel is a group of rivals who agree to act like that single owner. They hold total volume down, keep the price up, and split the volume. Each member’s share of the volume is its quota. Together they earn the monopoly profit, and each takes a slice.
Why each member wants to break it. Here is the catch. At the cartel price, each gallon sells for much more than it costs. So every extra gallon a station pumps looks very profitable — to that station. If one station secretly pumps more than its quota, the total rises, and the price falls a little for everyone. The cheater sells more gallons at a slightly lower price, and it comes out ahead. The loyal station sells the same gallons at the lower price, and it loses. The cheater gets all of the gain from its extra gallons but pays only part of the price damage. The rest of the damage lands on its rival.
If everyone cheats, everyone loses. Each station reasons the same way. If both pump more, the total rises a lot and the price falls a lot. Both end up below the deal. Each station acted in its own interest, and both are worse off. That is why most cartels fall apart.
The same story with prices. Gas stations usually compete with the number on the sign, not with gallons. The temptation looks the same. Undercut the agreed price and you pull drivers from your rivals for a while. But if your rivals see the cut, they answer it. One rival matches. Another goes even lower. Now you are earning less than before, round after round. A cut that rivals see and copy pays only once. Each round after that costs you.
So when does a deal last? Holding a high price is easier when a cut is seen and answered fast, because then cutting buys almost nothing. That happens when:
- there are few sellers, so each one can watch all the others;
- the product is identical, so a price gap is the only reason to switch;
- prices are visible — on a pole sign, a website, a published list;
- sales happen often and in small amounts, so a cut shows up in days, not months.
With many sellers, secret contract prices, and products that differ, a cut can go unseen for a long time. Then coordination is weak, and prices stay closer to cost.
The legal line. An explicit agreement to fix prices — a phone call, an email, a meeting where rivals agree on a price — is illegal in the United States and in most countries. But rivals who simply watch each other’s posted prices and match them, with no agreement, are usually not breaking the law. Economists call this tacit coordination. The outcome can look the same; the legal status is very different.
What this means for your memo. When you write about your company’s rivals, describe what you can see and cite it: “Rivals matched our last two price cuts within a week.” Never write that anyone is “fixing prices” — you have no evidence of an agreement, and matching is not an agreement. Then draw the pricing conclusion: in a market where cuts are seen and matched fast, the risk of starting a price war is high.
Market demand P = a − b·Q, marginal cost c, n members.
Cartel volume Q = (a − c) ÷ (2b) · cartel price P = a − b·Q · each member’s quota = Q ÷ n
Gross profit for one station = (P − c) × its gallons (× 1,000 when gallons are in thousands)
One member sells more than its quota → total Q rises → P falls for everyone.
Try it
Part A: the cheat panel. The example opens on two stations at Exit 41.
- Leave the extra at 1.0 thousand gallons. Read the three bars. Who gains, who loses, and what happens if both stations cheat?
- Slide the extra up to a full quota (3.0). Does cheating alone still pay more than the deal?
- Switch to “Undercut the posted cartel price” and try a $0.05 cut. Why does the loyal station drop to $0?
- Change the number of stations to 3 or 4. Is the cheater’s gain bigger or smaller than with two?
Part B: price war vs. the bots. You are one of four stations. Your rivals are three scripted bots. Play five rounds. Then play again with a different plan. How each bot decides is revealed after round 5. Rehearse here before you set your price in the class price war.
Worked example
Problem. Exit 41 (fictional) has two stations. Market demand is P = 6.90 − 0.30·Q, where Q is total thousand gallons a day. Each gallon costs the station $2.90 wholesale plus $0.40 in card fees and handling, so c = $3.30. What is the cartel deal, what does a cheater earn, and what happens if both cheat?
Step 1. The deal. Q = (6.90 − 3.30) ÷ (2 × 0.30) = 3.60 ÷ 0.60 = 6 thousand gallons. P = 6.90 − 0.30 × 6 = $5.10. Quota: 3 each. Each station earns (5.10 − 3.30) × 3 × 1,000 = $5,400 a day.
Step 2. One station cheats. It pumps 4 while the other keeps 3. Total Q = 7. P = 6.90 − 0.30 × 7 = $4.80. Cheater: (4.80 − 3.30) × 4 × 1,000 = $6,000 (up $600). Loyal station: 1.50 × 3 × 1,000 = $4,500 (down $900).
Step 3. Both cheat. Each pumps 4. Total Q = 8. P = 6.90 − 2.40 = $4.50. Each earns 1.20 × 4 × 1,000 = $4,800 — both below the $5,400 deal.
Step 4. The price version. Now four stations with partly loyal drivers (the price-war game). All at $6.00: each earns $90 a round. One station cuts to $5.00 while three hold $6.00: the cutter earns $100. Then it goes back to $6.00, but one rival has copied its $5.00 and another has dropped to $4.50 and stays there. Its five rounds: 100 + 65 + 75 + 75 + 75 = $390. Holding $6.00 for all five rounds: 5 × 90 = $450. One good round, four worse ones.
Step 5. Will a deal last here? Two stations, identical gasoline, prices on a pole sign, sales every day. Any cut is seen at once and matched, so cutting buys little. Holding a high price is easy here — and the price-war risk after a cut is high.
Check yourself
Two stations at an exit agreed to pump 3 thousand gallons a day each and sell at $5.10. Demand is P = 6.90 − 0.30·Q (Q = total thousand gallons) and each gallon costs $3.30. One station secretly pumps 4. What is its daily gross profit?
Cheating alone pays: the cheater sells more at a price that falls only a little.
Same exit: the deal is 3 thousand gallons each at $5.10 ($5,400 each a day). What happens if BOTH stations secretly pump 4?
One cheater gains; when everyone cheats, the price falls and all are below the deal.
In which market is it hardest for rivals to keep prices high without any agreement?
Coordination without an agreement needs few sellers, similar products and prices everyone can see.
For memo Section 4 you found that both main rivals matched your company’s last two price cuts within a week. Which sentence belongs in the memo?
An explicit agreement is illegal; watching and matching posted prices usually is not, so describe the behavior and cite it.
Four stations each earn $90 a round at $6.00. You cut to $5.00 for one round and earn $100. You go back to $6.00, but one rival has dropped to $4.50 and stays there, so you earn $65 in round 2 and $75 in each of rounds 3, 4 and 5. What is your five-round total?
A cut that rivals see and answer pays once and costs you in every round after.
Video
Video coming soon.