Shape 08
Zero-Sum
A strictly competitive situation where one side's gain is exactly the other's loss.
Two practical consequences. First, mixing becomes optimal: where an opponent profits precisely by predicting you, unreadability is the strategy, and any pattern at all — including strict alternation, which feels random and is not — is exploitable. Second, and more important in practice, most disputes people describe as zero-sum are not. Negotiations usually have differing priorities that permit trade; the zero-sum framing destroys value that was available and is often adopted for rhetorical rather than analytical reasons.

- How it feels
- Add up what both sides get in any outcome and it is always the same total.
- There is genuinely nothing both parties would prefer to the status quo.
- The other side benefits precisely and only by predicting you.
- Nobody is proposing trades, because there is nothing to trade.
- Who is playing
- Two sides — and, very often, a third party who is being fought over rather than fought with, and who has a strategy of their own that neither side has counted.
- Where it lands
- The value of the game, split by how well each side mixes. Skill decides it and there is no surplus to divide.
- What moves it
Look for the differing priorities that make trade possible; if you find none, randomise properly and stop leaking pattern. And be suspicious of anyone insisting a negotiation is zero-sum, because that framing usually serves somebody.
Not to be confused with
Nearly every misread in practice is a shape mistaken for its neighbour — and each of those mistakes points you at the wrong fix.
Positive-Sum
Is there any outcome you would BOTH prefer to today? If there is, it is not zero-sum, and treating it as such destroys the thing you both wanted.
Bargaining
Are you fighting over the size of the pie or the split? The split is zero-sum; growing it is not, and most negotiations contain both.
Where you have already met it
Sport and Competition
Penalty kicks. The keeper's only job is to predict, so the taker's only job is to be unpredictable.
Crime and Policing
Where the patrol car parks tonight. Inspection games are the practical form of this shape.
Law and Courts
The division of a fixed award. Genuinely zero-sum — which is why the real negotiation is usually about everything except the number.
Politics and Voting
Seats in a fixed-size chamber. One of the few political quantities that really is fixed, which is why redistricting is so brutal.