We have recently produced a trimmed-down version of this model in the article attached:
Stackelberg Attack on Protocol Fee Governance.pdf (422.5 KB)
The streamlined Grim Forker smart contract permits LPs to commit to reallocating their reserves—given certain triggers—away from the AMM to a fork with a hardcoded protocol fee of 0%.
This kind of smart contract produces a modified equilibrium between LPs allocating their reserves and Governance setting the AMM protocol fee. Under our simplified model, we prove how the new equilibrium benefits LPs and how it is rational for them to participate in the smart contract.
Note on references: This kind of commitment game (with Stackelberg equilibria) between governance and a protocol stakeholder has been already studied in context of stablecoins [2109.08939] Decentralized Governance of Stablecoins with Closed Form Valuation and we hope this work can help expanding the boudaries. We call our setup a Stackelberg Attack in the wake of [2305.02178] Stackelberg Attacks on Auctions and Blockchain Transaction Fee Mechanisms.