Game Theory · Diagnosis Clinic A · ← Lesson 04

Which game is this?

Every exercise so far told you which tool to use. Real decisions never do. This is the rep that actually matters — diagnosing the shape before you solve.

~12 min · after Lessons 01–04 Skill: picking the right lens cold Format: unlabeled cases

WHY THIS EXISTSThe tool you reach for first is the whole game

You now own four lenses. Lesson 01: the dominance test — is one move best no matter what they do? Lesson 02: value the matrix — payoffs are preferences, and you must model their objective. Lesson 03: iterated dominance — cross off their bad options, then yours. Lesson 04: best response & Nash — when nobody has a dominant move, hunt the stable pair.

Below are six situations from your real world, stripped of their labels. For each, the first job isn't to solve it — it's to name the lens. Misdiagnose the shape and every clever calculation after it is wasted. Answer, then read why.

THE CASESSix unlabeled decisions

Case 1

Whatever the rival clinic does about price, running your seasonal promo brings you more booked consults than skipping it — in the world where they promote too, and in the world where they don't.

Which lens?

Dominance test (L01). "Better whatever they do" is the exact fingerprint of a dominant strategy. You don't need to predict them at all — you just play it. Textbook one-liner: if a move wins in every column, stop analysing and do it.

Case 2

You're about to write off a price fight because "it'd hurt their bottom line as much as mine, so they'll fold." But that clinic pays its doctors on patient volume, not margin.

Which lens catches the mistake you're about to make?

Value the matrix (L02). The error is filling their cells from your chair. Paid on volume, a price war is their comfort zone — so "they'll fold to protect profit" is exactly backwards. Ask "what do they optimise?" before you write a single one of their numbers.

Case 3

A competitor could set five different prices, but three sit below their own cost — no rational operator would ever pick them. Rule those out and your own choice suddenly gets obvious.

Which lens?

Iterated dominance (L03). You're not finding your own dominant move — you're deleting their dominated options first, which shrinks the game until your choice falls out. "Cross off what a rational opponent would never do, then re-look" is the iterated move.

Case 4

On a shared keyword, your best bid depends on the rival's bid, and theirs depends on yours. Neither of you has a move that's best regardless. You're trying to find the pair where neither would want to change unilaterally.

Which lens?

Best response & Nash (L04). "No dominant move; my best depends on theirs" is precisely when dominance runs out and you switch to best-response reasoning. The answer is the Nash pair — the standstill where neither profits from moving alone.

Case 5 · the trap

A patient books you because a friend recommended you and it "felt right." Nothing in your pricing, ads, or positioning changes how they reason — they're not responding to your move at all.

Which lens?

Not a game (L02 contraindication). A "player" has to be choosing in response to you. A patient acting on gut and word-of-mouth isn't strategic — this is a decision under uncertainty, modelled as odds, not a rival's best response. Forcing a matrix here invents an opponent that doesn't exist.

Case 6 · the other trap

You set your keyword bid first. The rival sees it, then chooses their bid in response — and you knew they would when you moved.

Which lens?

Sequential — a game tree (L06, coming up). It is a game, but the moves aren't simultaneous: one commits, the other reacts. A grid throws away the order that drives everything. You "look forward and reason backward" down a tree instead — which is exactly Lesson 06. Spotting that a matrix is the wrong representation is half the skill.

THE TELLHow to tell them apart in five seconds

If you catch yourself thinking…	Reach for
"This move wins no matter what they pick"	Dominance test (L01)
"Wait — what do they actually want here?"	Value the matrix (L02)
"They'd never rationally do X or Y — drop those"	Iterated dominance (L03)
"My best move depends on theirs, and vice versa"	Best response & Nash (L04)
"They're not really reacting to me at all"	Not a game — model it as odds
"One of us clearly moves first and the other sees it"	Game tree (L06)

The clinic's one idea

In the wild, the hardest step isn't solving the game — it's naming which game you're in. Diagnose the shape first; the right tool is then obvious, and the wrong tool can't quietly ruin your answer.

YOUR REPDiagnose a real one, cold

Do this before you next solve anything. Open DECISIONS.md, pick a row, and — before reaching for any matrix — write one line: which of the six shapes above is it? Dominance, model-their-payoffs, iterated, Nash, not-a-game, or sequential?

Then say why in a sentence, and only then solve it. If two of us disagree on the diagnosis, that's the most useful conversation to have — bring it to me.

The gate: the win here isn't getting six quiz answers right — it's catching yourself, on a live decision, before you grab the wrong tool. Log the first time you do.