Reference · Cheat Sheet 01
The Dominance Test
First law of strategic thinking: never play a strictly dominated strategy — and assume a rational opponent won't either.
The 4-step routine for any strategic decision
- Is it even a game? Does your best move depend on someone else's choice? If no → it's a plain decision, just optimise. If yes → continue.
- Lay out the matrix. Your options as rows, theirs as columns. In each cell write
(your payoff, their payoff). Payoffs = everything you each care about, ranked.
- Hunt for dominance — on both sides. For each of your strategies, ask: is another strategy of mine always at least as good and sometimes better? If one option beats another no matter what they do, the loser is dominated. Do the same from their seat.
- Eliminate & predict. Cross out dominated strategies (yours and theirs). If you're left with one row and one column → that's the predicted outcome. If a single strategy beats all your others against everything → it's dominant: play it.
What you're looking for
Dominant strategy ✓
Best for you against every opponent move. Rare and precious — when you have one, you don't even need to predict them. Just play it.
Dominated strategy ✗
Worse than some other option of yours against every opponent move. Never play it. The mistake amateurs make is keeping it "just in case."
Worked example — the discount trap (a prisoner's dilemma)
You vs. a rival clinic. Each cell = (your monthly profit, their profit), in thousands. Higher = better.
| They hold price | They discount |
|---|
| You hold price | (10, 10) | (2, 14) |
|---|
| You discount | (14, 2) | (5, 5) |
|---|
If they hold, you earn 14 by discounting vs 10 by holding → discount. If they discount, you earn 5 by discounting vs 2 by holding → discount. Discount dominates. By symmetry they reason identically, so you both discount and land on (5, 5) — worse for both than (10, 10). Individually rational, collectively worse. That's the trap.
The strategic lever: "they'll surely hold" is wishful thinking, not strategy. The matrix tells you the trap is real. Escaping it needs a structural change — repetition, a credible commitment, a binding contract, or changing the payoffs — which is exactly where later lessons go.
Traps to avoid
- Optimising your move in a vacuum. Always check the opponent's column first.
- Confusing "good outcome" with "dominant".
(10,10) is the nicest cell but it is not what dominance predicts — don't plan around outcomes neither side has an incentive to choose.
- Eliminating a weakly dominated strategy carelessly. If it only ties (never strictly worse), be cautious — the order you eliminate can change the answer.