地下水市场中的按比例分配机制
Pro-rata mechanisms in groundwater markets
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中文总结 AI 辅助
本文针对地下水市场供需失衡问题，扩展已有价格形成模型提出按比例配给机制，结合外生限制、主从博弈场景展开理论分析与数值验证，还与多种非对称配给方案对比，为市场监管提供了工具。
中文摘要 AI 辅助
本文引入一种按比例配给机制以解决地下水市场的供需失衡问题，对Cialenco与Ludkovski（2025）的价格形成模型进行了扩展。研究表明，在按比例分配机制下，任意价格均为纳什均衡，因此当供需不匹配时，按比例分配方法可作为一种配给手段。该机制的本质决定了供需失衡的解决方式是唯一的，且这种比例配给方法具有公平性。首先，我们考虑存在外生限制的市场，即每个代理人的买卖数量受到限制，推导了最优消费的闭式解，并刻画了单边上限如何单调改变帕累托价格，而双边上限则会产生模糊影响。这些结果为做市商（或监管机构）提供了一种工具，用于研究交易限制对价格形成的影响。其次，我们研究了一种主从博弈场景，其中监管机构作为领导者，通过优化自身目标（如平衡社会福利与目标交易量，或公平目标如衡量农户盈利能力的基尼型差异指标）来设定交易价格，而农户作为“追随者”则通过按比例分配交易做出响应。我们还将提出的按比例分配方法与一系列非对称配给方案（基于优先权、基于超额量、统一及混合按比例规则）进行了比较，这些方案在比例公平性与对小型或资深水权持有者的保护之间进行权衡。我们通过一个针对简化的四农户地下水市场校准的数值案例研究，对所有理论结果进行了说明。
英文摘要
We introduce a pro-rata rationing mechanism for resolving supply-demand imbalances in groundwater markets, extending the price-formation model of Cialenco and Ludkovski (2025). We show that under the pro-rata distribution, every price is a Nash equilibrium, thereby pro-rata approach provides a rationing device whenever supply and demand fail to match. By the very nature of the pro-rata mechanism, the resolution of supply-demand imbalances is unique, and the proportional rationing approach is fair. First, we consider markets with exogenous restrictions on the amounts each agent may buy and/or sell, deriving closed-form first-best consumption and characterizing how one-sided caps monotonically shift the Pareto price, while two-sided caps have an ambiguous effect. These results give the market-maker (or regulator) a tool for studying the impact of trading restrictions on price formation. Second, we study a leader-follower setting in which a regulator (the leader) sets the trading price by optimizing first its own objective, such as balancing social welfare against a target traded volume or a fairness objective such as Gini-type disparity measure across farmers' profitability, while farmers (the `followers') respond via pro-rata trading. We further compare the proposed pro-rata approach to a family of asymmetric rationing schemes (seniority-based, excess-based, uniform, and mixed pro-rata rules) that trade off proportional fairness against protections for small or senior water-rights holders. Throughout, we illustrate the theoretical results with a numerical case study calibrated to a stylized four-farmer groundwater market.
