动态对抗资源分配：dDAB游戏
Dynamic Adversarial Resource Allocation: the dDAB Game
AI总结：
本文提出动态Defender-Attacker Blotto游戏，扩展经典静态Blotto游戏到图上的动态资源分配问题。研究确定 defender 资源的必要和充分数量以保证持续防御，并构建相应策略。通过可达性分析和集动态规划算法实现最优策略。
摘要：
本文介绍了动态Defender-Attacker Blotto（dDAB）游戏，将经典静态Blotto游戏扩展到图上的动态资源分配设置。在dDAB游戏中， defender 需要在连接图的关键节点上保持数量优势。游戏以离散时间展开，双方轮流重新分配资源，资源每次只能移动一跳。主要目标是确定保证持续防御所需的 defender 资源数量及相应策略。为解决图约束下的资源重新分配挑战，我们进行了可达性分析，从简化设置开始，其中攻击者资源作为单一群体。然后扩展框架以允许攻击者资源任意分裂和合并，并利用叠加原理构建 defender 策略。开发了基于集的动态规划算法来计算最优策略及最小 defender 资源量以确保成功防御。通过数值模拟和在Georgia Tech Robotarium平台上的硬件实验验证了方法的有效性。
英文摘要：
This work introduces the dynamic Defender-Attacker Blotto (dDAB) game, extending the classical static Blotto game to a dynamic resource allocation setting over graphs. In the dDAB game, a defender is required to maintain numerical superiority against attacker resources across a set of key nodes in a connected graph. The engagement unfolds as a discrete-time game, where each player reallocates its resources in turn, with resources allowed to move at most one hop per time step. The primary goal is to determine the necessary and sufficient amount of defender resources required to guarantee sustained defense, along with the corresponding strategies. To address the central challenge arising from graph-constrained resource reallocation, we conduct a reachability analysis, starting with simplified settings where attacker resources act as a single cohesive group. We then extend the framework to allow attacker resources to split and merge arbitrarily, and construct defender strategies using superposition principles. A set-based dynamic programming algorithm is developed to compute the optimal strategies, as well as the minimum amount of defender resources to ensure successful defense. The effectiveness of our approach is demonstrated through numerical simulations and hardware experiments on the Georgia Tech Robotarium platform.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
