AI 中文总结
该研究针对含两资产两交易者的无费用封闭式CFMM经济，推导了单边均衡的帕累托最优性、代表性代理人存在条件，证明交易可收敛至帕累托最优均衡，并给出首轮交易先动优势的相关条件。
AI 中文摘要
我们研究具有两种资产和两个交易者的封闭式、无费用常函数做市商（CFMM）经济中的均衡。内部状态是单边无交易均衡，当且仅当CFMM边际价格等于两个交易者的边际替代率。对于内部初始状态，个体理性的单边均衡相对于固定的CFMM不变量是帕累托最优的。在每个固定均衡处，通过加权上卷积得到弱代表性代理人，而当交易者具有共同的同质性偏好时，存在与状态无关的强代表性代理人。每个内部可行状态可通过有限次有效交易实现，且交替进行的效用最大化交易收敛到帕累托最优的单边均衡。我们还推导了交易顺序在首轮产生先动优势或劣势的条件。
英文摘要
We study equilibria in a closed, fee-free constant-function market maker (CFMM) economy with two assets and two traders. An interior state is a unilateral no-trade equilibrium exactly when the CFMM marginal price equals both traders' marginal rates of substitution. For an interior initial state, individually rational unilateral equilibria are Pareto optimal relative to the fixed CFMM invariant. A weak representative agent is obtained at each fixed equilibrium by weighted sup-convolution, whereas a state-independent strong representative agent exists exactly when traders share a common homothetic preference. Every interior feasible state is reachable through finitely many valid trades, and alternating utility-maximizing trades converge to a Pareto optimal unilateral equilibrium. We also derive conditions under which trading order produces a first-mover advantage or disadvantage in the first round.
