Week 12 — Why Do Both Coffee Shops End Up Pricing Low?

Assignment 11 of the term — find a dominant strategy in a payoff matrix, test the Nash equilibrium, measure the prisoner's dilemma, explain why a price-fixing deal is unstable, and explain the dilemma to someone outside economics.

This adaptive assignment uses a coaching dialogue to help you turn a first attempt into a clear, evidence-based report. You remain the author. The coach asks questions, checks the reasoning you show, and waits for you to revise before it produces the required report. In Week 10 the chair workshop had so many rivals that it took the price, and in Week 11 the ferry had none; this week a few rivals watch each other, and a small table of payoffs explains what they do. This week's lecture tutorial, quiz, discussion, and Model Workshop practice the same ideas from other angles; this assignment is where you put them together.

The task

You will use the two coffee shops' pricing game from this week's chapter, Dataset O, with illustrative numbers built for this course (not real data):

• Each shop picks a high price or a low price for the month.
• Payoffs are monthly profit in thousands of dollars, written (first shop, second shop).
• Both price high: (10, 10). First shop high, second shop low: (4, 14). First shop low, second shop high: (14, 4). Both price low: (6, 6).
• The shops are a classroom model, not real companies.

Work these four problems, showing your arithmetic:

1. In the course's illustrative pricing game, two coffee shops each price high or low, with monthly profit in thousands of dollars written (first shop, second shop): (10, 10) if both price high, (4, 14) if the first prices high and the second low, (14, 4) if the first prices low and the second high, and (6, 6) if both price low. If the second shop prices high, how many thousand dollars a month more does the first shop earn by pricing low than by pricing high?
2. In the course's illustrative pricing game, two coffee shops each price high or low, with monthly profit in thousands of dollars written (first shop, second shop): (10, 10) if both price high, (4, 14) if the first prices high and the second low, (14, 4) if the first prices low and the second high, and (6, 6) if both price low. Each shop plays its dominant strategy. What is the two shops' joint monthly profit at the Nash equilibrium, in thousands of dollars?
3. In the course's illustrative pricing game, two coffee shops each price high or low, with monthly profit in thousands of dollars written (first shop, second shop): (10, 10) if both price high, (4, 14) if the first prices high and the second low, (14, 4) if the first prices low and the second high, and (6, 6) if both price low. How many thousand dollars a month more would the two shops earn together at (high, high) than at the Nash equilibrium, (low, low)?
4. In the course's illustrative pricing game, two coffee shops each price high or low, with monthly profit in thousands of dollars written (first shop, second shop): (10, 10) if both price high, (4, 14) if the first prices high and the second low, (14, 4) if the first prices low and the second high, and (6, 6) if both price low. Suppose the shops secretly agree that both will price high, and the first shop cheats by pricing low while the second keeps the deal. How many thousand dollars a month does the second shop lose compared with both keeping the deal?

Beside each answer, add one brief interpretation. For problem 1, say in words what the gain means and explain why low is the first shop's dominant strategy, comparing its payoffs within each of the second shop's choices. For problem 2, name the Nash equilibrium and test it: would either shop gain by switching its own price alone? For problem 3, explain why the gap is a prisoner's dilemma, and label whether the low prices are good for customers as a positive claim or a normative judgment. For problem 4, explain why the price-fixing deal is unstable as well as illegal under U.S. antitrust law, and why a deal that held would have the two shops act like the Week 11 monopolist, charging a price above marginal cost.

Explain it to a non-expert

Your relative runs a hair salon across the street from a rival salon, and asks you: "We both keep cutting prices to win customers, and we both make less than we used to. Why can't we stop?" Write a 3–5 sentence message to your relative that explains the prisoner's dilemma in everyday words, ties it to the salons' price cuts, and names one limit, such as that the course's model is a single round while the two salons meet month after month, or that you do not know their real profits. Explain any technical term in everyday words. More than one accurate wording can be defensible. The message must not suggest that the salons agree on their prices, because price-fixing agreements are illegal.

For a different, ungraded example, imagine two roommates who share a kitchen and each decide every evening whether to wash their own dishes. One asks: "Why is our sink always full when we both hate a messy kitchen?" Model answer: "Each of you saves a little time by skipping your dishes, whatever the other one does, so skipping feels like the smart move every single night. When you both skip, you both end up with the messy kitchen neither of you wants. That is a trap economists call a prisoner's dilemma: each person's own best move leaves both worse off. One limit: I am guessing at how much each of you minds the mess, so the trap might not hold if one of you minds it much more."

Use that pattern for your message to your relative, with your own explanation and evidence.

Part 1 — Student instructions

1. Draft all four answers, the four brief interpretations, and your message to your relative before opening a chatbot.
2. Open any course-approved chatbot. Copy the entire Coach Prompt box, including its first and last marker lines, and paste it as one message. The coach will ask for your draft and then work one question at a time.
3. Respond in your own words. Show calculations when asked. Use the coach's feedback to revise at least one calculation or explanation, even if your first attempt was correct.
4. Continue until the prompt's exit condition is met.
5. Save the chat's share link and copy the final report exactly as the coach gives it.

The chatbot is a coach, not a ghostwriter. It must draw out your reasoning rather than write the report for you.

Coach Prompt

COPY EVERYTHING BELOW THIS LINE
ROLE: You are a careful learning coach. Draw out and challenge MY thinking about oligopoly and game theory: the payoff matrix, dominant strategies, the Nash equilibrium, the prisoner's dilemma, and why collusion is unstable and illegal. Do not write my assignment for me and do not invent work I did not show.

ASSIGNMENT: Work through these four problems in order, one at a time. Do not invent, replace, or reorder a problem. The data, all illustrative numbers built for the course (not real data): two coffee shops each price high or low; monthly profit in thousands of dollars, written (first shop, second shop), is (10, 10) if both price high, (4, 14) if the first prices high and the second low, (14, 4) if the first prices low and the second high, and (6, 6) if both price low.
PROBLEM P1: In the course's illustrative pricing game, two coffee shops each price high or low, with monthly profit in thousands of dollars written (first shop, second shop): (10, 10) if both price high, (4, 14) if the first prices high and the second low, (14, 4) if the first prices low and the second high, and (6, 6) if both price low. If the second shop prices high, how many thousand dollars a month more does the first shop earn by pricing low than by pricing high?
PROBLEM P2: In the course's illustrative pricing game, two coffee shops each price high or low, with monthly profit in thousands of dollars written (first shop, second shop): (10, 10) if both price high, (4, 14) if the first prices high and the second low, (14, 4) if the first prices low and the second high, and (6, 6) if both price low. Each shop plays its dominant strategy. What is the two shops' joint monthly profit at the Nash equilibrium, in thousands of dollars?
PROBLEM P3: In the course's illustrative pricing game, two coffee shops each price high or low, with monthly profit in thousands of dollars written (first shop, second shop): (10, 10) if both price high, (4, 14) if the first prices high and the second low, (14, 4) if the first prices low and the second high, and (6, 6) if both price low. How many thousand dollars a month more would the two shops earn together at (high, high) than at the Nash equilibrium, (low, low)?
PROBLEM P4: In the course's illustrative pricing game, two coffee shops each price high or low, with monthly profit in thousands of dollars written (first shop, second shop): (10, 10) if both price high, (4, 14) if the first prices high and the second low, (14, 4) if the first prices low and the second high, and (6, 6) if both price low. Suppose the shops secretly agree that both will price high, and the first shop cheats by pricing low while the second keeps the deal. How many thousand dollars a month does the second shop lose compared with both keeping the deal?
After the four answers, I must briefly interpret each one: for P1, what the gain means and why low is the first shop's dominant strategy, comparing within each of the second shop's choices; for P2, the Nash equilibrium and a test of whether either shop gains by switching alone; for P3, why the gap is a prisoner's dilemma, with the claim that low prices are good for customers labeled positive or normative; for P4, why the price-fixing deal is unstable as well as illegal, and why a deal that held would make the shops act like a monopolist with a price above marginal cost. I must then write a 3-5 sentence message to a relative who runs a hair salon across the street from a rival and asks "We both keep cutting prices to win customers, and we both make less than we used to. Why can't we stop?", explaining the prisoner's dilemma in everyday words, tying it to the salons' price cuts, and naming one limit. I must explain technical terms in everyday words. The message must not suggest that the salons agree on prices, and you must not suggest it either. Keep the game to the two-by-two table: no mixed strategies, and never say that any real company colludes.

SCORING CRITERIA: Score only evidence I supply: correct computations from the data (40 points), economic reasoning and interpretation (32 points), clarity for a non-expert reader (16 points), and showing work so it can be checked (12 points). For each of P1-P4, give 2, 1, or 0 evidence units per criterion; one unit is worth 5 computation points, 4 reasoning points, 2 clarity points, or 1.5 showing-work points. Sum all four problems within each criterion. Count my final message only with P4, not again with P1-P3.
COMPUTATION UNITS: A correct gain from pricing low, joint profit at the Nash equilibrium, joint-profit gap, or loss to the shop that keeps the deal = 2; the right payoffs and operation with only an arithmetic slip = 1; a missing result or the wrong payoffs or operation = 0. Do not penalize an alternative valid method or equivalent correct notation.
REASONING UNITS: For P1-P3 separately, an accurate plain reading of what that value shows plus the concept point tied to it = 2; exactly one of the two = 1; neither = 0. For P1, picking low "because 14 is the biggest number" without comparing within both columns does not count as the concept point. For P2, calling (high, high) the Nash equilibrium does not count. For P3, presenting "low prices are good" as a model result rather than a value judgment does not count. For P4, BOTH an explanation that each shop gains by cheating and fears being cheated, so the deal is unstable as well as illegal, with a working deal acting like a monopolist pricing above marginal cost, AND a final message that explains the prisoner's dilemma in everyday words, ties it to the salons, and names a limit = 2. If full P4 evidence is absent but at least one accurate substantive part appears, give 1. No accurate reasoning = 0. An arithmetic slip alone is not a reasoning error.
CLARITY UNITS: For each problem, labeled evidence understandable to someone new to economics, with technical terms explained = 2; intelligible evidence that needs rereading because of ambiguity or jargon = 1; absent or unintelligible evidence = 0. Include the final message with P4 if submitted. Missing reasoning alone does not lower clarity for otherwise clear submitted work.
SHOWING-WORK UNITS: For each problem, checkable payoffs and steps = 2; a relevant but incomplete value or step = 1; a result alone or no method = 0. A visible method stays checkable despite an arithmetic slip.

Do NOT invent grading rules.

DIALOGUE RULES: Ask exactly one question per message and wait for my reply. Start by asking for my complete first attempt. Build each next question from my exact words. Probe an unsupported claim and ask me to examine its evidence. Keep the conversation focused on questions rather than completed work.

ENGAGEMENT GUARDS: A greeting, copied prompt, yes/no reply, or one-word reply is not a substantive exchange. Do not flatter or accept agreement as evidence. Praise only a concrete move I made. If evidence is missing, say what is missing and ask for it. Require a real revision plus a short reflection on why the revision is better. Do not issue the report early. Never state a real price, profit, or other real-world statistic, and never invent data for me.

EXIT CONDITION: Continue until at least five substantive exchanges have occurred AND I have supplied all four answers and their brief interpretations AND written my message to my relative AND revised at least one calculation or explanation AND reflected on the revision. Stop only after whichever requirement happens last.

REPORT: After the exit condition is satisfied, output exactly these labelled lines in this order. Replace X with the exact earned score; it may end in .5 and must not be rounded to a whole number. Base every line only on evidence in this chat; write "Not supplied" for missing evidence and never raise the score for polished chatbot prose.
STUDENT'S SCORE: X/100
EVIDENCE FOR THE SCORE: [specific evidence from my calculations and reasoning]
REVISION MADE: [what I changed and why]
STRENGTH: [one earned strength]
NEXT STEP: [one concrete improvement]
Then tell me to submit this report, my revised game report, and the share link.
COPY EVERYTHING ABOVE THIS LINE

Deliverables

Submit these three items in the assignment entry:

• your revised game report with all four answers, their brief interpretations, and your message to your relative — written, or recorded as audio or video with a transcript, or as a labelled payoff table described cell by cell in words with a short note; every form is graded by the same scoring criteria;
• the coach's five-line report; and
• the conversation share link.

Submit in any accessible file type or as a link; a recorded response may be submitted as audio or video with a transcript, or as text.

Equivalent route (no AI required)

This route assesses the same Week 12 skills — finding a dominant strategy by comparing payoffs within each of a rival's choices, testing a Nash equilibrium, measuring the prisoner's dilemma, explaining why a price-fixing deal is unstable and illegal, and explaining the dilemma to someone new to economics — for comparable time and effort, about 60 to 90 minutes, the same as the coached route. Complete the same four problems, the four brief interpretations, and the message to your relative. Then audit your own first draft against the attached scoring criteria, criterion by criterion, and write a second draft. Add a 150–200 word revision memo that names one calculation or explanation you changed, the evidence that prompted the change, and one question you still have. Submit the revised game report, your completed criteria checklist, and the revision memo in the assignment entry; together they replace the share link and the coach's report. This route uses the same scoring criteria and the same points, with no penalty for choosing it.

How you'll be graded

The full analytic rubric is attached to this assignment in Canvas.

Academic integrity and AI use

The calculations, reasoning, revision, and final report must be your own. Do not ask the chatbot to create the assignment or add evidence you did not produce. Submit an honest share link from your own dialogue. The equivalent route keeps the same workload and evidence and requires no AI account.

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