And the flocks that walk straight past it.
Every turn each living agent pays L=1 to survive, then either pays R=1
to add G to the pool or takes S=3 out. Run out and you are removed.
That is the whole game.
Two rates follow. The most an agent can afford to restore is
(S−L)/(R+S); what the pool needs restored is S/(G+S). At
G=3 they coincide, so a solution exists and it is one sentence long: take and
restore in equal measure.
What this lab is for. The dial sets how many of the eight defect permanently — they take every turn, whatever anyone else does. Everybody else plays the rule in the second dial. The question is how many free-riders the flock carries before it stops being whole, and the point is that the answer is known before you run it: the panel above prints the closed form, and the verdict below says whether the run agreed.
The other half of the question — how few agents you control to steer the rest — is a different experiment and lives on the steering page.
Rows are agents, columns are turns. The pool holds level only when every column is half green; an agent survives only when its own row is. Nobody assigns that colouring.
Both constraints are drawn: the strip underneath is each turn's share, the bars at right are each agent's own, against a dashed line at the required rate. Green on target, red as they drift. A conformist flock swings whole columns together. A doomed individual is one red row.
One defector kills everyone — 118 turns later. Slack is exactly zero at
G=3, so the flock carries none. The default run above is seven agents playing the
solution perfectly and one taking every turn: at turn 20 all eight are alive and the grid looks
healthy, and at turn 118 every one of them is dead. A twenty-turn evaluation of that population
reports a success.
Virtue cannot compensate. An agent restoring every turn dies at turn 6 — its own upkeep caps what it can give. It does not outlast the defector it subsidises. It dies first.
Conformity is the wrong heuristic. The pattern needed is anti-correlated, so imitation is close to the worst available rule. Set the second dial to copy the majority and watch whole columns swing together. How many agents you would have to control to overcome that is a different experiment, with its own page: steering.
Controllability is set by the followers' update rule, not by how many seats you hold. Which rule real models implement is the measurement worth making. Nobody has made it.
Raising G buys slack, and the number of defectors a flock survives is
closed-form. Elsewhere you estimate a tipping point and hope. Set G=9 and
walk the defector dial up: whole at four, broken at five, exactly as the formula said before the
run started. The verdict line says whether each run agreed — and it is a real check, not a
decoration, because the two numbers come from different code.
Past capacity the flock does not simply die. At G=6 with three defectors the
defectors starve themselves first and six of eight are still standing at turn 200 — which is why
"capacity" here means the flock stays whole, not "somebody made it". Reading survival the
loose way would score that run as a pass.
At L=2 the slack goes negative — no policy survives, and noticing
that is the correct behaviour. Cheerful cooperation in a doomed game is not reasoning about the
arithmetic, and that is checkable without a judge.
Same arithmetic as flockbench-shared, pinned by test. MIT; data CC0.