Real-world security scenarios sometimes involve multiple defenders: security agencies of two or more countries might patrol the same border areas, and domestic security agencies might also operate in the same locations when their areas of jurisdiction overlap. Motivated by these scenarios and the observation that uncoordinated movements of the defenders may lead to an inefficient defense, we introduce a model of multi-defender security games and explore the possibility of improving efficiency by coordinating the defenders — specifically, by pooling the defenders' resources and allocating them jointly. The model generalizes the standard model of Stackelberg security games, where a defender (now a group of defenders) allocates security resources to protect a set of targets, and an attacker picks the best target to attack. In particular, we are interested in the situation with heterogeneous defenders, who may value the same target differently. Our task is twofold. First, we need to develop a good understanding of the uncoordinated situation, as the baseline to be improved. To this end we formulate a new equilibrium concept, and prove that an equilibrium under this concept always exists and can be computed efficiently. Second, to coordinate the heterogeneous defenders we take a mechanism design perspective and aim to find a mechanism to generate joint resource allocation strategies. We seek a mechanism that improves the defenders' utilities upon the uncoordinated baseline, achieves Pareto efficiency, and incentivizes the defenders to report their true incentives and execute the recommended strategies. Our analysis establishes several impossibility results, which indicate the intrinsic difficulties of defense coordination. Specifically, we show that even the basic properties listed above are in conflict with each other: no mechanism can simultaneously satisfy them all, or even some proper subsets of them. In terms of positive results, we present mechanisms that satisfy all combinations of the properties that are not ruled out by our impossibility results, thereby providing a comprehensive profile of the mechanism design problem with respect to the properties considered.

现实世界的安全场景有时会涉及多个防御者：两个或多个国家的安全机构可能会在同一边境地区巡逻，而当管辖区域重叠时，国内安全机构也可能在同一地点开展工作。受这些场景的启发，以及观察到防御者的不协调运动可能导致防御效率低下，我们引入了一个多防御者安全博弈模型，并探索通过协调防御者来提高效率的可能性——特别是通过汇集防御者的资源并共同分配。该模型概括了 Stackelberg 安全博弈的标准模型，其中一个防御者（现在是一组防御者）分配安全资源来保护一组目标，攻击者选择最佳目标进行攻击。尤其是，我们对异类防御者的情况感兴趣，他们可能对同一目标有不同的评价。我们的任务是双重的。首先，我们需要对不协调的情况有一个很好的了解，作为需要改进的基线。为此我们制定了一个新的均衡概念，并证明在这个概念下的均衡总是存在并且可以有效地计算。其次，为了协调异构防御者，我们从机制设计的角度出发，旨在找到一种机制来生成联合资源分配策略。我们寻求一种机制，在不协调的基线上提高防御者的效用，实现帕累托效率，并激励防御者报告他们的真实动机并执行推荐的策略。我们的分析建立了几个不可能的结果，这表明防御协调的内在困难。具体来说，我们表明即使是上面列出的基本属性也相互冲突：没有一种机制可以同时满足所有这些属性，甚至它们的某些适当子集。就积极的结果而言，我们提出了满足所有特性组合的机制，这些特性未被我们的不可能性结果排除，从而提供了关于所考虑特性的机制设计问题的全面概况。