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Back-run Effects in Private Routing for Cryptocurrency Trading on the Blockchain

Author

Listed:
  • Taiga Saito

    (Faculty of Economics, Hitotsubashi University)

  • Akihiko Takahashi

    (The University of Tokyo)

  • Shivam Gupta

    (Neoma Business School)

Abstract

This study formulates, for the first time, the back-running mechanism in private routing for on-chain cryptocurrency trading as a leader–follower stochastic differential game between a user and a trusted searcher, providing practical implications for the mechanism design of on-chain market infrastructure. We propose a model to investigate the effect of back-running by a trusted searcher in private routing for a user in on-chain cryptocurrency transactions. The continuous-time linear–quadratic (LQ) leader–follower stochastic differential game is solved via a forward–backward stochastic differential equation (FBSDE) approach using the stochastic maximum principle. Numerical examples illustrate how allowing back-running affects the market impact of the cryptocurrency and the user's total purchasing cost under different liquidity conditions in the on-chain market. This helps infrastructure companies design healthier markets by allowing users to choose whether to provide trade information to trusted searchers.

Suggested Citation

  • Taiga Saito & Akihiko Takahashi & Shivam Gupta, 2026. "Back-run Effects in Private Routing for Cryptocurrency Trading on the Blockchain," CIRJE F-Series CIRJE-F-1279, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2026cf1279
    as

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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2026/2026cf1279.pdf
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    References listed on IDEAS

    as
    1. Paul Janicot & Alex Vinyas, 2025. "Private MEV Protection RPCs: Benchmark Stud," Papers 2505.19708, arXiv.org.
    2. Yu Zhang & Yafei Li & Claudio Tessone, 2025. "A Line Graph-Based Framework for Identifying Optimal Routing Paths in Decentralized Exchanges," Papers 2504.15809, arXiv.org.
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