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A groundwater market model

Igor Cialenco, Michael Ludkovski

TL;DR

The paper frames groundwater pumping as a multi-agent trading problem within basins, where farmers maximize revenue from crop production and water trades under water-right constraints and intertemporal banking. It derives a Nash equilibrium characterization in the one-period setting and connects the Pareto-optimal price to market-clearing, showing that the shadow value of water aligns with a central-planner optimum under centralized allocation. Extending to a two-period setting, banking introduces intertemporal competition; the authors solve for equilibria via dynamic programming and best-response fixed points, illustrating how banking affects prices and profits and highlighting regulatory roles. The work lays theoretical and computational groundwork for groundwater markets, with a companion study proposing scalable, ML-inspired methods to solve multi-period dynamic Nash games in larger basins. Its significance lies in informing policy design for sustainable groundwater management under SGMA-like regimes by clarifying price formation, trading incentives, and the effects of water banking.

Abstract

We introduce the problem of groundwater trading, capturing the emergent groundwater market setups among stakeholders in a given groundwater basin. The agents optimize their production, taking into account their available water rights, the requisite water consumption, and the opportunity to trade water among themselves. We study the resulting Nash equilibrium, providing a full characterization of the 1-period setting and initial results about the features of the multi-period game driven by the ability of agents to bank their water rights in order to smooth out the intertemporal shocks.

A groundwater market model

TL;DR

The paper frames groundwater pumping as a multi-agent trading problem within basins, where farmers maximize revenue from crop production and water trades under water-right constraints and intertemporal banking. It derives a Nash equilibrium characterization in the one-period setting and connects the Pareto-optimal price to market-clearing, showing that the shadow value of water aligns with a central-planner optimum under centralized allocation. Extending to a two-period setting, banking introduces intertemporal competition; the authors solve for equilibria via dynamic programming and best-response fixed points, illustrating how banking affects prices and profits and highlighting regulatory roles. The work lays theoretical and computational groundwork for groundwater markets, with a companion study proposing scalable, ML-inspired methods to solve multi-period dynamic Nash games in larger basins. Its significance lies in informing policy design for sustainable groundwater management under SGMA-like regimes by clarifying price formation, trading incentives, and the effects of water banking.

Abstract

We introduce the problem of groundwater trading, capturing the emergent groundwater market setups among stakeholders in a given groundwater basin. The agents optimize their production, taking into account their available water rights, the requisite water consumption, and the opportunity to trade water among themselves. We study the resulting Nash equilibrium, providing a full characterization of the 1-period setting and initial results about the features of the multi-period game driven by the ability of agents to bank their water rights in order to smooth out the intertemporal shocks.
Paper Structure (8 sections, 1 theorem, 27 equations, 2 figures, 1 table)

This paper contains 8 sections, 1 theorem, 27 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. The Model
  3. Equilibrium water rights price
  4. One period market model
  5. Illustrative Example and Comparative Statics
  6. Multi-period Market
  7. Role of trading and banking
  8. Conclusions

Key Result

Proposition 2.2

Assume that $\underline{c}_j\leq \theta_j R=W_j$ for all $j$. Then, for any $p\geq 0$, there exists $\boldsymbol{\pi}$, such that $(\boldsymbol{\pi}, p)$ is a NE.

Figures (2)

  • Figure 1: One-period groundwater market with two agents and two goods. Left: groundwater consumption amounts $C_j(p)$ as a function of water price $p$. Shaded area indicates the prices for which trades occur. Efficient price $p^\circ=0.975$ corresponds to setting $\mathfrak{C}(p^\circ) = \mathfrak{W}$ (horizontal gray line) total available water. Horizontal dotted lines indicate farmer individual allocations $W_1, W_2$. Right: optimal production quantities $\varphi_j^{k,*}(p)$ given groundwater market price $p \in [0.1, 2.5]$.
  • Figure 2: Left: Best response curves $\bar{b}_{-j} \mapsto B_j( \bar{b}_{-j})$ for the two-period market with 2 farmers. The unique crossing point $(3.367, 2.142)$ corresponds to the equilibrium banking strategies. Right: impact of banking, with the last column listing the equilibrium total profit, $A^*_j = V_j(0) + \mathbb{E}[ V_j(1) | R(0)]$.

Theorems & Definitions (7)

  • Definition 2.1
  • Proposition 2.2
  • proof
  • Remark 2.3
  • Remark 3.1
  • Remark 3.2
  • Remark 3.3