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Proof of Stake economy under centralized exchanges--a mean field model

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  • Wenpin Tang

Abstract

We consider the interaction between centralized trading and decentralized Proof of Stake (PoS) blockchain ecosystems. Motivated by the increasing dominance of centralized exchanges and the institutionalization of crypto markets, we study how trading activities on centralized exchanges affect staking behavior, token allocation, and decentralization within a PoS blockchain. We formulate a continuous-time mean field model, where the miners simultaneously act as validators in the PoS protocol and traders in a centralized market with price impact. Under suitable assumptions, we establish the local well-posedness of the mean field system, and derive a semi-explicit characterization of the equilibrium trading strategy. Numerical results suggest that centralized trading activities may enhance staking participation, and promote decentralization of the staking distribution through market incentives. We also study the effects of transaction costs and token supply mechanisms on the equilibrium staking ratio and concentration profile. These results illustrate how market microstructure and centralized liquidity provision can exert significant influence on decentralized blockchain protocols.

Suggested Citation

  • Wenpin Tang, 2026. "Proof of Stake economy under centralized exchanges--a mean field model," Papers 2606.09003, arXiv.org.
    • Handle: RePEc:arx:papers:2606.09003
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    References listed on IDEAS

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    1. Ruofei Ma & Zhebiao Cai & Wenpin Tang & David Yao, 2025. "Optimal Decisions for Liquid Staking: Allocation and Exit Timing," Papers 2507.14810, arXiv.org, revised Dec 2025.
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    4. Wenpin Tang & David D. Yao, 2022. "Trading under the Proof-of-Stake Protocol -- a Continuous-Time Control Approach," Papers 2207.12581, arXiv.org, revised Jun 2023.
    5. Wenpin Tang, 2022. "Stability of shares in the Proof of Stake Protocol -- Concentration and Phase Transitions," Papers 2206.02227, arXiv.org.
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    10. Wenpin Tang & David D. Yao, 2023. "Trading under the proof‐of‐stake protocol – A continuous‐time control approach," Mathematical Finance, Wiley Blackwell, vol. 33(4), pages 979-1004, October.
    11. Cartea, Álvaro & Drissi, Fayçal & Monga, Marcello, 2025. "Decentralised finance and automated market making: Execution and speculation," Journal of Economic Dynamics and Control, Elsevier, vol. 177(C).
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