EIGENFLOW: Optimal Market Making on Directed Acyclic Graph Blockchains

This paper extends the classical Avellaneda-Stoikov framework for optimal market making to blockchain networks with directed acyclic graph (DAG) structure. In DAG-based consensus protocols such as GHOSTDAG, multiple blocks are produced in parallel, creating a branching time structure that fundamentally alters the market maker's optimization problem.

We derive a DAG-extended Hamilton-Jacobi-Bellman equation that incorporates the probability distribution over transaction acceptance, showing that optimal spreads depend on the anticipated ordering of parallel blocks. Our main theoretical result demonstrates that market makers achieve O(1/n) variance reduction in inventory risk by distributing quotes across n parallel execution paths, exploiting the transaction-level mutual exclusivity inherent to GHOSTDAG ordering.

We extend the framework to K correlated assets (proving portfolio-level variance reduction of O(K/n)) and provide adversarial robustness analysis under bounded hash power attacks. Implementation analysis for the Kaspa network (10 BPS, k=124 post-Crescendo) addresses practical constraints including direct-to-miner submission requirements, fee incentive compatibility, and latency bounds.

Monte Carlo simulations validate theoretical predictions, showing Sharpe ratio improvements of 40-82% over single-path strategies under realistic network conditions. This work establishes foundational theory for high-frequency decentralized finance applications on DAG-based blockchains.