Problem
Research questions and friction points this paper is trying to address.
equilibrium
constant-function market maker
marginal rates of substitution
Pareto optimal
unilateral no-trade
Equilibrium in closed constant-function market maker economies
🤖 AI Summary
研究了无费用恒定函数做市商经济中两位交易者的均衡问题，通过边际价格和替代率分析，提出了一种达到帕累托最优的交易方法。
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
constant-function market maker
marginal rate of substitution
Pareto optimality
unilateral equilibrium
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