Equilibrium in closed constant-function market maker economies

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Highly relevant for understanding DeFi/AMM market microstructure, price impact mechanics, transaction ordering effects (MEV-adjacent), and optimal execution in CFMM-based exchanges. The first-mover advantage/disadvantage analysis directly informs trading strategy in decentralized exchanges. However, the closed-market, fee-free, two-asset benchmark limits direct applicability to production trading systems. The equilibrium characterization and reachability results provide theoretical foundations for understanding AMM dynamics.

The theoretical framework requires advanced knowledge of convex analysis, general equilibrium theory, and differential geometry of level curves. Implementing the numerical examples (alternating utility-maximizing trades, computing indifference prices, verifying equilibrium conditions) is moderate. The proofs are technically demanding but the computational aspects (solving tangency conditions, iterating best responses) are straightforward for standard CFMM functions.

The paper is fully theoretical with complete proofs provided in appendices. Numerical examples (Tables 1-4, Examples 2-8) use standard CFMM functions (log-product, constant-product) with explicit parameters, making them reproducible. However, no code repository is provided. The mathematical framework is self-contained with all assumptions clearly stated.