2019, Set 1, Question 3 · 6 points
2019 AP Microeconomics FRQ 3 (Set 1) answers
Pizzeria advertising and entry game
Use a payoff matrix to find the jointly best outcome, test each firm's incentive to cheat, check for a dominant strategy and find the Nash equilibrium. Rebuild the matrix after a side payment and find the new equilibrium.
Skip to the worked answer and scoring (try the question first if you can)
This exam had three free-response questions in a 60 minute section (10 minutes of reading and 50 of writing), with about half the time suggested for Question 1 and the rest split evenly between Questions 2 and 3. The current exam has 3 free-response questions in 60 minutes. The skills these questions practice still count.
Lessons this question draws on
1 Read the question
The question is College Board's, from the 2019, Set 1 exam. It starts on page 4 of the PDF. College Board no longer posts this exam, so it opens from the copy of College Board's PDF that the Internet Archive saved on December 20, 2025.
2 Write your answer
Answer each part the way you would on the exam, in full sentences, with your work shown. Your writing saves as you type.
3 Score it
Score your answer against College Board's scoring guidelines, one point at a time. Give yourself a point only when your answer says what the guideline asks for.
Scoring guidelines (PDF, page 6) What the exam readers saw (Chief Reader report)
4 Worked answer and scoring
Here is how a response that earns full credit could read, part by part, and what College Board's scoring guidelines look for, put in our own words. Open a part once you have written your own answer to it. The scoring guidelines PDF above is the official word on every point.
Read each cell as (Patrick's profit, Dee's profit). For any question about one player's choice, hold the other player's action fixed and compare that player's own payoffs only. A Nash equilibrium is a cell where neither player can do better by changing its own action alone.
Part a 1 point
Model answer
Patrick's Pie advertises and Dee's Pizzeria stays out. The combined profits are $48 (Advertise, Enter), $175 (Advertise, Stay Out), $165 (Do Not Advertise, Enter) and $100 (Do Not Advertise, Stay Out), and $175 is the largest.
What earns the point
- Patrick's Pie advertises and Dee's Pizzeria stays out. Adding the two profits in each cell, $175 + $0 = $175 is the largest total. The answer names the two actions, not the payoffs in the cell.
Part b 1 point
Model answer
Neither has an incentive to cheat. With Patrick advertising, Dee earns $0 by staying out and would earn −$2 by entering, so entering lowers Dee's profit. With Dee staying out, Patrick earns $175 by advertising and would earn $100 by not advertising, so Patrick also loses by switching.
What earns the point
- Neither firm would cheat: Dee's profit would fall from $0 to −$2, and Patrick's from $175 to $100. Cheating means one firm changing its own action while the other keeps its part. Each firm's alternative pays it less, and the explanation needs those numbers for both firms.
Part c 1 point
Model answer
No. If Dee enters, Patrick does better not advertising ($150 against $50). If Dee stays out, Patrick does better advertising ($175 against $100). Patrick's best action depends on what Dee does, so no single action is best in every case.
What earns the point
- Patrick's Pie has no dominant strategy. A dominant strategy is best whatever the other player does. Patrick's best choice changes with Dee's, so neither action qualifies.
Part d 1 point
Model answer
There are two Nash equilibria:
- Patrick does not advertise and Dee enters ($150, $15). Patrick would earn $50 by advertising instead, and Dee would earn $0 by staying out instead.
- Patrick advertises and Dee stays out ($175, $0). Patrick would earn $100 by not advertising instead, and Dee would earn −$2 by entering instead.
In the other two cells at least one firm gains by switching.
What earns the point
- Two Nash equilibria: Do Not Advertise with Enter, and Advertise with Stay Out. Testing every cell for a profitable one-player switch leaves these two. A game need not have a dominant strategy to have a Nash equilibrium, and it can have more than one.
Part e 2 points
Model answer
(i) The $20 moves from Patrick to Dee only in the cells where Dee stays out: Patrick's payoff there falls by $20 and Dee's rises by $20. The Enter column is unchanged.
(ii) Staying out now pays Dee $20 whatever Patrick does, more than either −$2 or $15 from entering, so Dee stays out. Knowing that, Patrick compares $155 from advertising with $80 from not advertising and advertises. The one Nash equilibrium is Patrick advertises and Dee stays out ($155, $20).
What earns each point
- The matrix redrawn with both players and all four actions, and with $20 taken from Patrick and given to Dee in both Stay Out cells: $155, $20 and $80, $20. The payment happens only when Dee stays out, whatever Patrick does, so only that column changes. The Enter cells keep their original payoffs.
- The Nash equilibrium is Patrick's Pie advertises and Dee's Pizzeria stays out. Staying out is now Dee's dominant strategy, and against it Patrick earns more by advertising, so neither firm gains by switching from that cell.
Common mistakes
From what the exam readers reported seeing in 2019 students' answers, in our words:
- Answering with the payoffs in a cell, such as "$175, $0", instead of the actions the two firms take.
- Saying neither firm would cheat without numbers from the matrix to show it.
- Not reading off each firm's own best option to see whether it gains by switching alone.
- Naming only one Nash equilibrium when this game has two.
- Not knowing how to find a Nash equilibrium when neither player has a dominant strategy.
- Not redrawing the matrix correctly after the $20 payment.
- Picking the wrong cell as the Nash equilibrium of the redrawn matrix.
Question, scoring guidelines and Chief Reader report: College Board, from the Internet Archive. The title, summary and worked answer are ours.