> ## Documentation Index
> Fetch the complete documentation index at: https://docs.kalarislabs.com/llms.txt
> Use this file to discover all available pages before exploring further.

> ## Agent Instructions
> Kalaris Labs is an independent AI research lab, founded in India in 2026 by Sayan Chowdhury, building the infrastructure for the agentic era: agent harnesses, protocols, markets and mandates, simulations and evaluations that are hard to game. Its motto is "The rules have to exist before the actors do." Answers to common questions are at https://docs.kalarislabs.com/lab/faq.
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# Liquidity Coupling: stopping insolvency cascades in agent networks

> Escrowing a fraction of each contract stops insolvency cascades when AI agents hire agents. In a 10,000-agent simulation, mean cascade depth fell by 70.2%.

**Bottom line:** When AI agents hire other agents, one default at the bottom of the chain can travel upward faster than a person can intervene. Liquidity Coupling has the delegating agent escrow a fraction α of each payment for downstream creditors. Once α is above a threshold set by the branching factor, cascades die out.

| | |
| - | - |
| **Author** | Sayan Chowdhury ([ORCID 0009-0004-8421-0087](https://orcid.org/0009-0004-8421-0087)), Kalaris Labs |
| **Published** | 2026-11 on Zenodo (preprint) |
| **Evidence** | Results come from simulation. |
| **DOI** | [10.5281/zenodo.24121189](https://doi.org/10.5281/zenodo.24121189) |
| **License** | CC BY 4.0 |
| **Theme** | [Agent economies](https://docs.kalarislabs.com/research.md#agent-economies) |

> [card] [Read the paper](https://zenodo.org/records/24121189)
>
> Full text (02\_Liquidity\_Coupling.pdf) and versions on Zenodo.

> [card] [Code](https://github.com/KalarisLabs/liquidity-coupling-)
>
> Source on GitHub: `liquidity-coupling-`.

> [card] [Agent economies series](https://docs.kalarislabs.com/research/agent-economies.md)
>
> Related Kalaris Labs documentation.

## Key points

* The paper names the **Recursive Default Problem**: a worker fails, its hirer cannot pay the sub-contractors it already engaged, and the hirer's own hirer is exposed in turn.
* Modelled as a branching process with mean branching factor λ, each default transmits upward with probability 1 − α. The cascade dies out with probability one when α ≥ 1 − 1/λ, and has finite expected size 1 / (1 − λ(1 − α)) when α > 1 − 1/λ.
* A Markov inequality gives a tail bound on cascade size. Under a stated sub-linear extraction assumption, Sybil cartels that stake α·p per member are unprofitable once they are large enough.
* In a simulation with N = 10,000 agents and λ = 1.15 (100 trials per α), mean cascade depth fell from 4.7 at α = 0.05 to 1.4 at α = 0.20, a 70.2% reduction. The transition appears near the predicted α\_c = 0.1304.
* A small experiment on five-hop chains of locally served language models shows the same direction of effect.

## Limitations

All results are simulation or small-scale experiment, and the paper's empirical section lists what remains unverified. The reference repository's README describes an earlier version of the paper with different numbers; the Zenodo preprint is the current version.

## Abstract

> When AI agents hire other agents, a failure at the bottom of the chain can travel upward faster than any human can intervene. A worker fails, its hirer cannot pay the sub-contractors it has already engaged, and the hirer's own hirer is left exposed in turn. We call this the Recursive Default Problem. We propose Liquidity Coupling: a delegating agent escrows a fraction alpha of each contract's payment, which is released to downstream creditors if the worker defaults. Modelling the hierarchy as a branching process with mean branching factor lambda and homogeneous, locally tree-like structure, we show that each default transmits upward with probability 1 - alpha, so the cascade dies out with probability one when alpha >= 1 - 1/lambda and has finite expected size 1/(1 - lambda(1 - alpha)) when alpha > 1 - 1/lambda. A Markov inequality gives a simple tail bound on cascade size, and a short argument shows that Sybil cartels that stake alpha p per member are unprofitable once they are large enough, under a stated sub-linear extraction assumption. In a simulation with N = 10,000 agents and lambda = 1.15 (100 trials per value of alpha), mean cascade depth fell from 4.7 at alpha = 0.05 to 1.4 at alpha = 0.20, a reduction of 70.2%, and the transition appears near the predicted alpha\_c = 0.1304. A small experiment on five-hop chains of locally served language models shows the same direction of effect. All results are simulation or small-scale experiment; the empirical section lists what remains unverified.

## Related research

* [Orchestration Trilemma](https://docs.kalarislabs.com/research/papers/orchestration-trilemma.md): Agent markets face finite context, slow verification and fast default cascades at once. The Agent Coupling Protocol cut simulated systemic failure 8.1 to 14.2 times against four baselines.
* [Agent Coupling Protocol](https://docs.kalarislabs.com/research/papers/agent-coupling-protocol.md): ACP is a ten-stage protocol that weighs provider reliability more heavily as an orchestrator's context fills. In simulation, honest providers earn 4.8 to 7.6 times more than malicious ones.
* [Marginal Utility of Context](https://docs.kalarislabs.com/research/papers/marginal-utility-of-context.md): An exponential barrier price on context use makes a rational agent compress memory early. In a 50-agent simulation it raised task success from 0.42 to 0.73.

## Cite this paper

```bibtex theme={"system"}
@misc{chowdhury2026liquiditycoupling,
  title     = {{Liquidity Coupling in Autonomous Agent Networks: A branching-process threshold for systemic stability}},
  author    = {Chowdhury, Sayan},
  year      = {2026},
  publisher = {Zenodo},
  note      = {Preprint, Kalaris Labs},
  doi       = {10.5281/zenodo.24121189},
  url       = {https://doi.org/10.5281/zenodo.24121189}
}
```


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