Game Theory · Lesson 01

Think about their move,
not just yours

The first law of strategic thinking — and the one move that already separates you from most decision-makers.

~12 min · one sitting Skill: the dominance test Ties to: your real decisions

Before we start — no teaching yet, just commit

Before we start: if cutting price beats holding no matter what the rival does, what should you do?

01 · THE SHIFTWhen is a decision actually a game?

Most decisions you make all day are solo: pick the better option and move on. Which scalpel. Which font on the landing page. Whether to take an umbrella.

A game is different. A decision becomes a game the moment your best choice depends on what someone else chooses — and they're reasoning about you at the same time. That single property, strategic interdependence, is what game theory is about. Not competition. Interdependence.

If the right answer changes depending on what a thinking opponent does, you're in a game — and optimising your own move in a vacuum will quietly fail you.

Frame & vocabulary follow Open Yale ECON 159, Lecture 1 — "Five First Lessons" (Ben Polak). Full definitions live in your Glossary.

02 · THE PICTURESee the game: the payoff matrix

To reason about a game, you draw it. For two players, that's a payoff matrix: your options are rows, theirs are columns, and each cell holds (your payoff, their payoff) — higher is better. Payoffs bundle everything you each care about, not just money.

Here's one from your world. You and a rival clinic each decide, independently, whether to hold your consultation price or discount to grab volume. Numbers are monthly profit in thousands.

The discount standoff — each cell is (your profit, their profit).
	They hold	They discount
You hold	10, 10	2, 14
You discount	14, 2	5, 5

The gold number in each cell is your payoff — train your eye to read your own column of outcomes first.

Same reflex you already have A dominated strategy is a treatment that's worse on every endpoint and every subgroup — you never choose it. Spotting a dominated option is the same discipline as ruling out an inferior therapy: quick, decisive, no agonising.

03 · THE MOVEFind your dominant strategy

Now the actual technique. Don't ask "what do I hope they do?" Ask, for each thing they could do, what's best for you. Work it out — the buttons give instant feedback.

Reason it through

If they hold, you should…

If they discount, you should…

Notice what just happened: discount was better for you no matter what they did. That makes "discount" a dominant strategy. When you have one, you don't even need to predict the opponent — you just play it. And "hold" is strictly dominated: never play it.

The first law

Never play a strictly dominated strategy — and assume a rational opponent won't either.

Watch the sting, though. They reason exactly the same way, so both discount — landing you here:

Both sides apply dominance → the predicted outcome.
	They hold	They discount
You hold	10, 10	2, 14
You discount	14, 2	5, 5

You both end at (5, 5) — even though (10, 10), where you both held, was better for both of you. Two rational players, each playing their dominant strategy, walk straight into the worse outcome. That is the prisoner's dilemma, and price wars, ad-spend arms races, and over-prescribing races all share its shape.

The "individually rational → collectively worse" structure is laid out in the Stanford Encyclopedia — Prisoner's Dilemma.

04 · YOUR REPPractice — spot the dominant strategy

Fresh case, your world again. You and a rival clinic both bid on the same Google keyword. Each independently decides to run ads or pause. Cell = (your patients/month, their patients/month).

The keyword auction.
	They run	They pause
You run	6, 6	12, 4
You pause	4, 12	9, 9

Before you pick an option below — write it out: for each of their moves, what should you do and why?

Model answer: If they run: 6 (run) beats 4 (pause) → run. If they pause: 12 (run) beats 9 (pause) → run. Run beats pause in both columns, so run is your dominant strategy — you don't even need to guess what they'll do.

What is your dominant strategy?

05 · THE EYEGame, or just a decision?

The skill is also recognising when you're in a game at all. Tap your call — then read why. The trap is treating uncertainty (a forecast, a market) as if it were a strategic opponent.

Choosing which font to use on your landing page.

Setting your consult price when a clinic two blocks away will adjust theirs in response.

Deciding whether to schedule extra OR time based on the weather forecast for travel.

Negotiating a sponsorship for the skull-base course, where the sponsor weighs your ask against rival conferences courting them.

06 · KNOW THE LIMITSWhen the dominance test goes quiet

The dominance test is the fastest tool you have — but it only speaks when a strategy beats every column. Know when it falls silent, and don't force a verdict it isn't giving you.

When dominance goes quiet

No player has a dominant move. Most real games don't hand you one. When dominance is silent, you switch to best-response reasoning and Nash equilibrium — Lesson 04.
The game is sequential. If one side clearly moves first and the other sees that move before replying, this isn't a simultaneous grid — it's a game tree, Lesson 06. Reading a sequential move as a matrix will mislead you.
Don't overclaim dominance. "Best in some of their columns" is not dominance — it must win in every column, no exceptions. One column where it loses kills the claim.

Naming when the test goes quiet is what keeps it a real tool instead of a hammer you swing at everything.

07 · LOCK IT INWhat you can now do

Tell a game (strategic interdependence) from a plain decision — and not mistake uncertainty for an opponent.
Draw any two-player situation as a payoff matrix.
Run the dominance test: for each thing they could do, find your best reply; spot a dominant strategy (play it) or a dominated one (never play it).
Recognise a prisoner's dilemma — when individually rational moves trap both sides in a worse outcome.

Bring it back to me. Pick one real decision you're facing this week — a price, an ad budget, a course ask, a negotiation. Sketch it as a 2×2: your two options, their two options, rough payoffs. Then tell me:

① Does anyone have a dominant strategy? ② Is it secretly a prisoner's dilemma? I'll pressure-test your matrix with you — this is the part where it actually sticks. I'm your teacher here; ask me anything that was fuzzy, and I'll go deeper or slower.

Even better: open DECISIONS.md and use D3 — ads vs the competing clinic on shared keywords as your real case. It's the same shape as Section 04's keyword auction above, and DECISIONS.md already flags it as an auction-style prisoner's dilemma. Copy learning-records/REP-TEMPLATE.md to a new REP-D3-*.md and fill in Phase 1 before the rival's next move resolves it.

The gate: this lesson isn't "done" when you finish reading — it's done when one REP-*.md exists with Phase 1 filled. Delivered ≠ learned.

Primary sources: Open Yale ECON 159 (Polak) · SEP — Game Theory · SEP — Prisoner's Dilemma. Full list in RESOURCES.md.