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When do token systems stabilize? Compatibility constraints and community structure

  • Flore Sentenac
  • Mingwei Yang
  • Sophie H. Yu
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Abstract

Token systems support repeated service exchange without monetary transfers, but their viability depends on the stability of token balances. We study token systems with compatibility constraints among agents. A requester is randomly sampled in each period, and only a few randomly sampled agents are available to provide service. We establish a necessary and sufficient condition for stability and show that the minimum-token rule, which selects the available provider with the lowest token balance, achieves the optimal stability region. We then apply this stability criterion to a random token system generated from stochastic block models with uniformly sampled requesters. We tightly characterize the stability regime by identifying two obstructions to stability: insufficient service opportunities for a group of communities or for an individual agent.

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Cite

BibTeXRIS
BibTeX
@misc{sentenac2026when,
  title = {{When do token systems stabilize? Compatibility constraints and community structure}},
  author = {Flore Sentenac and Mingwei Yang and Sophie H. Yu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.36744},
  eprint = {2610.36744},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.36744},
}
RIS
TY  - UNPB
TI  - When do token systems stabilize? Compatibility constraints and community structure
AU  - Flore Sentenac
AU  - Mingwei Yang
AU  - Sophie H. Yu
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.36744
UR  - https://arxiv.org/abs/2610.36744
AB  - Token systems support repeated service exchange without monetary transfers, but their viability depends on the stability of token balances. We study token systems with compatibility constraints among agents. A requester is randomly sampled in each period, and only a few randomly sampled agents are available to provide service. We establish a necessary and sufficient condition for stability and show that the minimum-token rule, which selects the available provider with the lowest token balance, achieves the optimal stability region. We then apply this stability criterion to a random token system generated from stochastic block models with uniformly sampled requesters. We tightly characterize the stability regime by identifying two obstructions to stability: insufficient service opportunities for a group of communities or for an individual agent.
ER  -