Liquidity Coupling: stopping insolvency cascades in agent networks

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

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: 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: 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: 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

@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}
}