Lecture 31 — Strategy Under Uncertainty
Position in the course
This is lecture 31 of 32. It belongs to the course arc described in the course outline and uses the standard interactive case method: display, attempt (5 minutes), discuss, reveal, name the technique.
Learning objectives
- Frame decisions with payoffs and probabilities
- Use expected value to compare strategies
- Recognise when more information changes the decision
By the end of this lecture students can do all three under time pressure, which is what the four cases exercise.
Prerequisite knowledge
Before this lecture: Lectures 26 and 29 — probability and simulation
Assumed fluencies:
- expected value arithmetic
- simulation as an estimator
Preparation task: Compute the expected value of a 10-ticket lottery with published odds.
Detailed topic outline
Core (mandatory):
- expected value as a decision tool
- payoff tables
- the switch question resolved by listing
- risk aversion beyond expectation
Extension (optional enrichment):
- dominance arguments
- mechanism thinking: how rules shape behaviour
Case sequence
| Case | Title | Difficulty |
|---|---|---|
| cs-121 | The Umbrella Decision | Beginner |
| cs-122 | The Game Show Switch | Foundational |
| cs-123 | The Insurance Riddle | Intermediate |
| cs-124 | The Auction Bluff | Advanced |
Display each case full-screen from the student page (cases cs-121–cs-124); instructor pages cs-121–cs-124 under case-studies/instructor/ hold the full solutions, reveal guides, and discussion prompts.
Timing plan (120 minutes)
| Minutes | Segment |
|---|---|
| 0–10 | Framing: where this fits; recall of the previous lecture |
| 10–30 | Case 1 (cs-121): 5-minute attempt, then discussion and reveal |
| 30–50 | Case 2 (cs-122): same rhythm |
| 50–70 | Case 3 (cs-123): same rhythm, harder case |
| 70–75 | Break |
| 75–100 | Case 4 (cs-124): same rhythm, hardest case |
| 100–115 | Synthesis: name the techniques; misconceptions check |
| 115–120 | Exit questions, homework, next-lecture preview |
Timing flexes with the room: if a case ignites the class, let the discussion run and compress the synthesis; if the attempts stall, harvest partial attempts rather than extending the clock.
Worked examples
- cs-124 auction bluff: a payoff table completed for both bidders, dominant strategies found, and the equilibrium read off.
Instructor demonstration to open the lecture: Umbrella decision (cs-121): the payoff table drawn once, expected values computed twice — with rain 30% and 70%.
Classroom activities
| # | Activity | Minutes | Format and prompt |
|---|---|---|---|
| 1 | Payoff table gallery | 8 | Four decision scenarios turned into payoff tables; the class tours and votes on best actions. |
| 2 | Switch simulation | 7 | cs-122 played 30 times by pairs with forced switch vs forced stay; results pooled. |
| 3 | Risk interview | 5 | Same expected value, different variances: which do you choose? Answers are discussed, not graded. |
Board plan
- Left third: the case statement, kept visible for the whole cycle.
- Middle third: students' contrasting attempts (two maximum).
- Right third: the reference trace or table, revealed last.
- Bottom strip, written during the cycle: the name of the technique and the one-line invariant or rule this case taught.
Instructor explanation notes
Reading the room. Expected value is a decision tool, not a gambling lesson: the payoff-table discipline applies to project choices and policy. Risk attitudes are discussed, never mocked.
Running the reveal. cs-122's switch question is resolved by listing, the course's signature move, one last time.
Lecture focus. One sentence to repeat verbatim: Build the payoff table; let expectation argue, then judge risk.
Common misconceptions
- Comparing options on intuition when a payoff table is cheap.
- Reading expected value as a promise about a single outcome.
- Ignoring variance when stakes or ruin matter.
- Missing dominance that the payoff table would reveal instantly.
Each case's instructor page lists the specific wrong turn to expect; the reveal should address it by name.
Student practice exercises
Core:
- Build the umbrella payoff table (cs-121) for both rain probabilities and pick the action.
- List the six outcomes of the switch question (cs-122) and compute both strategies' expectations.
- Argue the insurance riddle (cs-123) from both sides: expected value says no, risk says yes.
Enrichment (optional):
- Design a fair mechanism for a shared fridge; analyse its equilibria informally.
- Compute the variance of cs-121's two options; connect to risk preference.
Formative assessment
Exit questions (choose one; answer on a card in 60 seconds):
- What does expected value compare, and what does it ignore? Expected: average outcomes; it ignores variance (risk) unless you add it
- Why does switching win in cs-122? Expected: the host's reveal leaks information; 2/3 of outcomes favour switching
- When is a dominated strategy visible instantly? Expected: one option's payoffs are worse in every column of the table
Cards are skimmed before the next lecture; three answers become the framing. Persistent wrong answers route students to the review stations of lecture 16 or to office hours.
Homework and preparation
- Before: skim the four student pages; attempt case 1 on paper.
- After: write a five-line pseudocode solution for any case you did not finish in class; bring one question to the next lecture.
- Enrichment (optional): the stretch question on each case page.
Learning-outcome mapping
- Primary outcomes: LO8, LO10 — Expected value and strategic reasoning.
- Coverage details: learning outcomes; assessed via the scheduled quizzes, labs, assignments, and term project in the assessment plan.
Differentiation
- Beginners: aim for a correct plan in pseudocode; Python is optional.
- Intermediate: full Python on cases 1–3, plan on case 4.
- Advanced students: finish early, then answer "what breaks at 10x scale?" and present the alternative-approach bullet from the instructor page.
- Everyone: state one assumption out loud before writing anything.