AI 中文总结
研究具有领导者-追随者框架的三人通用乐透游戏，推导追随者均衡收益与监管者NSE干预，开发带预算约束的多战场模型，通过数值模拟为监管者提供决策指导。
AI 中文摘要
在本文中，我们引入了具有监管者的通用乐透游戏（R-Lotto），它是经典两人通用乐透游戏的领导者-追随者扩展。该模型捕捉了竞争资源分配中的监管干预，监管者首先选择一个干预参数来影响两个资源受限的追随者之间随后的竞争。干预参数代表对其中一个追随者的偏袒，然后追随者进行带有偏袒的通用乐透子游戏。我们推导了追随者的均衡收益，并刻画了监管者的纳什-斯塔克尔伯格均衡（NSE）干预。我们进一步开发了一个具有监管者预算约束的多战场R-Lotto模型。在这种情况下，不同战场上的追随者子游戏是解耦的，而监管者的干预决策通过共同预算耦合。数值模拟证明了所提出的均衡刻画，并为监管者提供了实际决策指导。
英文摘要
In this paper, we introduce the General Lotto game with a regulator (R-Lotto), a leader-follower extension of the classical two-player General Lotto game. The model captures regulatory interventions in competitive resource allocation, where a regulator first chooses an intervention parameter to influence the subsequent competition between two resource-constrained followers. The intervention parameter represents favoritism toward one of the followers, and the followers then play a general Lotto subgame with favoritism. We derive the followers' equilibrium payoff and characterize the Nash--Stackelberg equilibrium (NSE) intervention of the regulator. We further develop a multi-battlefield R-Lotto model with a regulator budget constraint. In this setting, the follower subgames on different battlefield is decoupled, while the regulator's intervention decisions are coupled through a common budget. Numerical simulations demonstrate the proposed equilibrium characterizations and provide practical decision-making guidance for the regulator.
