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

Taiga Saito, Akihiko Takahashi and Shivam Gupta
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Taiga Saito: Faculty of Economics, Hitotsubashi University
Akihiko Takahashi: The University of Tokyo
Shivam Gupta: Neoma Business School

No CIRJE-F-1279, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

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.

Pages: 42 pages
Date: 2026-08
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Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2026cf1279

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