Accounting for externalities generated by fire spread is necessary for managing fire risk on landscapes with multiple owners. In this paper, we determine the optimal management of a synthetic landscape parameterized to represent the ecological conditions of Douglas-fir (Pseudotsuga menziesii) plantations in southwest Oregon. The problem is formulated as a dynamic game, where each agent maximizes their own objective without considering the welfare of the other agents. We demonstrate a method for incorporating spatial information and externalities into a dynamic optimization process. A machine-learning technique, approximate dynamic programming, is applied to determine the optimal timing and location of fuel treatments and timber harvests for each agent. The value functions we estimate explicitly account for the spatial interactions that generate fire risk. They provide a way to model the expected benefits, costs, and externalities associated with management actions that have uncertain consequences in multiple locations. The method we demonstrate is applied to analyze the effect of landscape fragmentation on landowner welfare and ecological outcomes.

中文翻译：

---

管理具有空间外部性的支离破碎的受火灾威胁的景观

考虑到火灾蔓延产生的外部性对于管理具有多个所有者的景观的火灾风险是必要的。在本文中，我们确定了参数化的合成景观的最佳管理，以代表俄勒冈州西南部花旗松 (Pseudotsuga menziesii) 种植园的生态条件。该问题被表述为一个动态博弈，其中每个代理最大化自己的目标而不考虑其他代理的福利。我们展示了一种将空间信息和外部性纳入动态优化过程的方法。机器学习技术，近似动态规划，用于确定每个代理的燃料处理和木材采伐的最佳时间和位置。我们估计的价值函数明确说明了产生火灾风险的空间相互作用。它们提供了一种方法来模拟与在多个地点具有不确定后果的管理行为相关的预期收益、成本和外部性。我们展示的方法用于分析景观破碎化对土地所有者福利和生态结果的影响。