cs-124 — The Auction Bluff
| Field | Value |
|---|---|
| id | cs-124 |
| difficulty | Advanced |
| topics | game theory, reasoning |
| lecture | lecture-31 |
| estimated time | 5-minute attempt + 10-minute discussion |
| prerequisites | functions, dictionaries, and earlier algorithmic patterns |
| objective | design the algorithm, verify it on edges, and argue correctness or trade-offs |
| solution | held by the instructor; discussed after the attempt |
Problem
A sealed-bid popup quiz auction for the last textbook. Reason one level up from naive bids; introduce thinking about others' thinking.
Your deliverable is the stated assumptions, the payoff computed for the worked instance, the second-price logic in one sentence, and one contested case. If the problem is ambiguous anywhere, state the assumption you are making and carry on — a stated assumption is part of a good answer.
Examples
- Input: one textbook; bids sealed; value to you 40; others bid 10-35 unknown
- Output: second-price logic: bid your true value 40; bidding higher risks overpaying, lower risks losing cheaply
Solve for the worked instance first. Then ask what would change if one number, name, or condition were replaced by something stranger.
What to notice
- Think one level up: what should OTHERS bid? Then choose the bid that does best against those choices.
- Writing the rules IS the solution; code is transcription.
- Every assumption is a place where two good answers can differ.
Discussion starter
After the solution is revealed, the class spends five minutes on this prompt: "Which assumption would you attack first if you had to argue the other side?"
Constraints and assumptions
- Difficulty: Advanced (functions, dictionaries, and algorithmic reasoning assumed).
- Topics: game theory, reasoning.
- Classroom-scale inputs unless the problem says otherwise.
- Time-box: about five minutes for a defensible plan; a complete solution may take longer and that is expected - state where you would resume.
- Optional stretch (not required): describe an alternative approach and say when it beats the obvious one.
Hints and extension
- First nudge: identify the pattern the worked instance uses before computing anything.
- If stuck after three minutes, write the input/output line you expect and trace the smallest example by hand.
- After the reveal, attempt the extension below before the next lecture.
- Extension challenge: Compute the flip point where the decision changes and defend the threshold.