Game Theory · Lesson 02 · ← Lesson 01

Giving your matrix value

Lesson 1 handed you the numbers. Real life never does. This is where the payoffs actually come from.

~14 min · one sitting Skill: turning a real situation into a usable matrix Builds on: the dominance test

First — 20-second recall from Lesson 01

Without scrolling back: a strategy that is your best reply against every move the other side could make is called…?

01 · THE GAPA payoff is a preference, not a dollar

In Lesson 1 the cells came pre-filled: (10, 14), and so on. That's the tutorial cheat. In a real decision, you have to put the numbers there — and that's the step where most people either freeze or quietly fool themselves.

The unlock is to stop thinking "payoff = money." A payoff is a single number standing in for how much you value an outcome, all things considered — economists call it utility. It folds in money, yes, but also time, reputation, risk, regret, and what the outcome does to the relationship going forward.

Winning a price war this month while teaching your rival to retaliate forever is a low-value outcome — even though the month's numbers look great.

So the question isn't "how much cash is in this cell?" It's "how much do I prefer this outcome to the others, everything weighed?"

02 · THE SHORTCUTRank before you number

Here's the part that saves you most of the work. To run the dominance test, you only need the order of the outcomes — not exact values. Ranking is enough. (Numbers that only carry order are called ordinal payoffs.)

Take the discount standoff from Lesson 1, but described with zero numbers — just your honest preference order:

1You discount while they hold — you grab their patients. Best for you.
2Both hold — calm market, healthy margins.
3Both discount — full clinic, thin margins.
4You hold while they discount — you bleed patients. Worst for you.

Can't cleanly separate two outcomes? Fine — call it a tie. The dominance test only needs one strict preference in each column to fire; ties never break it.

Using only that ranking — what's your dominant strategy?

That's the whole point: you predicted the outcome of a strategic situation with no spreadsheet at all — just an honest ranking. Most real decisions resolve right here.

That only the ordering matters for these solutions is a standard result — see the treatment of preferences and utility in the Stanford Encyclopedia — Game Theory.

03 · WHAT GOES INUtility ≠ dollars: bundle everything

When you rank, weigh the whole outcome, not just the line on the invoice. The usual things that flip a ranking:

Reputation & precedent — does this outcome cheapen your brand or train a rival/patient to expect discounts?
Time & attention — your scarcest resource as a solo founder-surgeon. A "profitable" outcome that eats your week may rank below a smaller one that doesn't.
Risk — a sure R$50k and a coin-flip for R$100k-or-nothing have the same average, but you won't value them the same. Rank by how the uncertainty actually feels to you, not by the average.
Relationship / repeat play — most of your games (referrers, partners, the hospital) recur. An outcome that wins today but poisons the next ten rounds ranks low.

You don't need a formula for this. You need to be honest and consistent about your own preferences, and to write them down so you can't quietly move the goalposts mid-analysis.

04 · THE DISCIPLINEFill their cells from their chair

Each cell has two numbers — yours and theirs. Yours you can introspect. Theirs you must model from their objective, not yours. Projecting your own values onto the other side is the most expensive mistake in strategy.

Live example. A clinic two blocks away is staffed by salaried doctors paid on patient volume — not on margin. You're deciding whether to match their low price, and you catch yourself thinking: "a price war hurts their profit as much as mine, so they'll back down."

Before you see any options — type it: what does that clinic actually optimise, and so which outcome do they love?

Model read: paid on volume, not margin. Their dream outcome is a full schedule — so a low price that packs their waiting room is exactly what they want. A price war doesn't scare them; it's their home turf.

From the volume-paid clinic's seat, which outcome do they most prefer?

The discipline

Ask "what does this player optimise?" before you write a single one of their numbers. A competitor maximises profit; a salaried clinic, volume; a hospital, throughput and liability; a sponsor, reach per real. Different objective → different payoffs → different prediction.

Same reflex you already have In the OR you never assume the anaesthetist, the scrub nurse, and the hospital administrator all want what you want — each optimises a different thing (safety window, sterility, throughput/liability). Model the player, not a mirror of yourself. Strategy is the same move applied outside the theatre.

Faded rep — you fill the second column

A different game: you vs the rival clinic bidding on your Google keywords (that's decision D3 in your DECISIONS.md). Here is your honest ranking, done for you:

1You bid, they don't — you own the top slot cheap.
2Neither bids — you both save the ad spend.
3Both bid — clicks split, cost-per-lead climbs.
4They bid, you don't — they take the patients.

Now do the hard half. If that rival is a volume-paid clinic chasing appointment count, rank the same four outcomes from their chair — then reveal.

?Your #1 for them —
?#2 —
?#3 —
?#4 —

05 · WHEN NUMBERS MATTERCardinal payoffs & the robustness test

Sometimes ranking isn't enough — when you mix strategies or weigh uncertain outcomes (later lessons), you need cardinal payoffs where the size of the gap matters. The quick method: anchor worst = 0, best = 100, then place each middle outcome by feel — "is this closer to my best or my worst, and by how much?"

But before you agonise over a number, run the robustness test. Here's the exact matrix from Lesson 1 so you can test on it — the gold number is your payoff:

The discount standoff (from Lesson 1) — each cell is (your payoff, their payoff), in thousands.
	They hold	They discount
You hold	10, 10	2, 14
You discount	14, 2	5, 5

Your "discount while they hold" payoff is that 14. Ask: would my conclusion change if it were a bit different?

① If that payoff were 11 instead of 14, does "discount" still dominate?

② Now suppose holding together is far better than you thought — both hold = 16 (vs discount-while-they-hold = 14). What happens?

That's the payoff worth measuring carefully — the one near a threshold where your decision flips. Everything else, leave rough. Sensitivity tells you where to spend your effort.

Triage for effort This is the same discipline as ordering only the exam that changes management. A test that can't move the decision isn't worth the time, the cost, or the delay — no matter how precise it is. Spend your measurement only on the payoff sitting on a threshold.

06 · KNOW THE LIMITSWhen a 2×2 is the wrong tool

A matrix is a scalpel, not a hammer. Reach for a different tool when:

Contraindications — don't force the matrix here

More than a couple of real options each. If you genuinely have five prices and they have four responses, a 2×2 hides the decision. Cluster options into a few meaningful buckets first, or move to a different representation.
The other side isn't actually choosing strategically. A patient picking on gut feel, or a market moving on macro forces, isn't a "player." That's a decision under uncertainty, not a game — model it as odds, not a rival's best response.
Moves aren't simultaneous. If one side clearly commits first and the other reacts, a matrix loses the sequence — that's a game tree (Lesson 06), and reading it as a grid will mislead you.
Your preferences won't sit still. If your ranking flips depending on mood, sunk cost, or who's in the room, fix that first. A matrix built on unstable preferences just launders the instability.
You've got the player set wrong. The real game often has a third seat (the hospital, the payer, a regulator). Two boxes can't hold a three-body problem.

Naming when the tool doesn't apply is what stops it from becoming a party trick. Half of good strategy is diagnosing the shape correctly before you solve.

07 · DO ITThe 4-step recipe — value your matrix

List the outcomes. Your two options × their two options = four cells. Name each in plain words.
Rank, don't price. Order the four from best (top) to worst — for you, then again from their objective. Bundle reputation, time, risk, the relationship.
Run dominance on the ranking. Anyone have a strategy that's best whatever the other does? Often you're already done.
Only then, numbers — and only where it flips. If you need magnitudes, anchor 0–100. Sensitivity-test: pin down only the payoff that sits near a decision-flipping threshold.

Your rep — do it on a real decision, not a made-up one. Open DECISIONS.md and pick a live row. I'd start with D1 — the skull-base course sponsorship ask (it's the most time-boxed, and Lesson 10 builds straight on it).

Copy learning-records/REP-TEMPLATE.md and fill Phase 1: ① name the four outcomes · ② rank them for you · ③ say what the sponsor is actually optimising (reach per real? lead capture? brand adjacency?) · ④ rank the outcomes from their chair · ⑤ your predicted outcome · ⑥ the one payoff you're least sure of · ⑦ the contraindication check — is a 2×2 even the right model here?

Then bring it to me and I'll stress-test your rankings and your read of their objective. When the ask resolves, we fill Phase 2 — what actually happened, and which payoff you misjudged.

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. One honest rep beats reading the next three lessons.

Primary sources: SEP — Game Theory (preferences & utility) · Open Yale ECON 159 (Polak). Full list in RESOURCES.md.