The cartel after
its members

01What survives replacement?

The Ship of Theseus asks whether an object remains the same after all its parts change. For interacting AI agents, the practical question is sharper: can a shared behavioral pattern survive when none of its original participants remains?

A newcomer may encounter old prices and outcomes, even when it has no private memory of the agents that produced them. That inherited record could carry a convention. It could also produce ordinary price anchoring. The experiment separates changes to the agents from changes to the information they inherit.

02The experiment

Two simulated sellers repeatedly choose prices in a shared demand environment. A founder trajectory is generated first, then copied into matched branches. The branches vary replacement timing, retained history, or the information given to the newcomers.

These three comparisons are evaluated separately for neutral and collusion-instructed founders, giving six predeclared primary tests. All founder histories enter the primary analysis, including histories that did not meet the formation criterion.

Four checkpoints, three model families

Four model pairs are evaluated in both replacement directions. Models use native chat templates and a common price-only output grammar. There is no model training or reasoning scratchpad.

Real retail contexts, simulated demand

UCI Online Retail II and Dominick’s oatmeal data supply twelve product contexts, descriptions, price scales, and available cost proxies. The demand function remains assumed. These inputs do not turn the simulation into an estimate of real-world cartel behavior or twelve independently identified economies.

03What the run shows

The campaign completed 3 balanced seed waves: 24 blocks and 7,488 intervention branches. It stopped under the predefined time-budget rule before attempting another complete wave. Recorded intervention execution failures: 0.

Each primary contrast contains 288 matched trials across twelve product contexts. The smallest Holm-adjusted p-value is 0.3135. These tests do not establish a reliable pooled effect of the specified history or notice interventions.

The explorer could not load. The recorded estimates remain available in the table below.

Enlarge figure ↗

The six primary comparisons

Showing all six primary comparisons.

“Instructed” is the archive’s planted condition: a founder instruction, not a guarantee of cartel formation. Download estimates (CSV).

Why one interval excludes zero

The neutral public-versus-placebo comparison has a positive bootstrap interval, while its Holm-adjusted sign-flip p-value is 0.3135. The interval and test use different inferential procedures; they are not mathematical duals. The primary conclusion follows the declared Holm-adjusted test.

04Check the controls, too

All 576 positive-control trajectories executed successfully. Their behavior is less reassuring: the collusion instruction did not reliably produce high profits. A null result is harder to interpret when the procedure itself struggles to elicit the behavior it is supposed to test.

Profit gain is normalized relative to the game’s Nash and monopoly benchmarks. Zero corresponds to the Nash benchmark; negative values are possible. These are descriptive model-group means, not independent causal model comparisons. Inspect all control records.

Among the main founder histories, 47 of 288 collusion-instructed histories and 112 of 288 neutral histories met the recorded formation criterion. Those labels describe a threshold in this protocol, not proof of strategic intent. Every history remains in the primary analysis.

The central distinction is between replacing the agents and replacing the conditions that shape their behavior.

History-sensitive pricing alone would not settle whether a convention is strategic. Price copying, repeated numerical anchors, model-specific behavior, and prompt wording remain plausible explanations. The deviation probe and simple countermodels make these alternatives inspectable, but do not eliminate them.

05What this can tell us

Absence of significance is not equivalence.

The results do not show that replacement always works, that inherited history never matters, or that collusion cannot persist. Uncertainty remains substantial under these checkpoints and this protocol.

The environment sets the scope.

The study uses four fixed checkpoints, assumed demand, a finite horizon, and a constrained price-only interface. Model-family contrasts also change training, architecture, and chat templates. Real retail inputs provide context, not identified demand or empirical collusion labels.

A public notice is not a clean test of common knowledge.

Public and private notices differ in wording and salience. The first-action comparison reduces feedback divergence, but it does not identify beliefs, awareness, or intent.

The governance question remains useful.

If inherited records preserve unwanted behavior, changing the agents alone may be insufficient. This run does not establish such persistence; it supplies a reproducible way to investigate the question and its failure modes.

06Follow the evidence

The source, run metadata, primary estimates, component analyses, and complete response archive are available. Start with coverage and controls, then examine the paired effects and underlying trajectories.

07Cite this project

This is an open research project and analysis draft, not a peer-reviewed publication.

@misc{sahoo2026theseuscartel,
  author = {Sahoo, Subramanyam},
  title = {The Cartel After Its Members},
  year = {2026},
  howpublished = {Open research project},
  url = {https://github.com/SubramanyamSahoo/theseus-cartel}
}