Lecture Notes — Lecture 31: Strategic Thinking Workshop
Companion to the lecture plan and the worked examples. Read the Definitions before class, the Explanation after it; the practice questions and the lecture quiz close the loop.
Definitions
- Strategy — a complete plan of action for every situation that might arise.
- Dominant strategy — one that is at least as good in every scenario - bid your true value in a second-price auction.
- Information set — what a decision-maker knows (and does not) at decision time; the host's knowledge changes everything.
- Best response — the optimal move given what others do - the one-level-up thinking the auction case trains.
- Equilibrium — a profile of strategies where nobody gains by changing alone; introduced informally.
Explanation
Strategy means a plan for every situation. Rock-paper-scissors has no fixed best move; the auction has a dominant one. The distinction seeds the whole session.
Second-price logic: bid your value. Overbidding risks paying too much; underbidding only risks losing wins you did not want at that price. The truth-telling property is derived from a two-bidder payoff table the class fills in.
The host's knowledge is the hidden assumption. Monty opens a door he KNOWS hides a goat. If the door were opened at random, switching gains nothing. Same script, different information - different strategy.
Best response as a habit. The popup-quiz auction trains 'think one level up': predict others' reasoning, then choose. Students write the other side's thinking before their own move.
Cheap talk vs commitment. In the group-project game, promises are free andbreakable; binding commitments change the game. Recognising which game you are in is the workshop's exit skill.
Examples
The lecture's worked examples live in examples.md; the case studies this lecture builds on are worked in class from the projector. The case sequence with difficulties:
Common misconceptions
- Playing a fixed move in games that require unpredictability.
- Assuming everyone sees the same information you do - the host's knowledge changes the game.
- Bidding above value 'to be safe' - the second-price table shows the exact risk.
- Treating promises as commitments; only binding actions change incentives.
Summary and key takeaways
- A strategy is a plan for every situation, not one move.
- Second-price auctions reward truthful bidding - derive, do not memorise.
- Information asymmetry changes optimal play.
- Think one level up: model the other side before moving.
Practice questions
- Fill the two-bidder second-price payoff table; circle the dominant strategy column.
- Play the popup auction with a hidden-value sheet; write the other side's reasoning before your bid.
- Redo Monty Hall assuming a random door opened (sometimes revealing the car); what happens to switching?
- Classify four provided scenarios: dominant strategy exists, or mixed/unpredictable play required.
Where this leads
Next lecture: Capstone: The Method Applied. The quiz below checks this lecture's essentials before we build on them.