Strategic decisions are often made over multiple periods of time, wherein decisions made earlier impact a competitor's success in later stages. In this paper, we study these dynamics in General Lotto games, a class of models describing the competitive allocation of resources between two opposing players. We propose a two-stage formulation where one of the players has reserved resources that can be strategically pre-allocated across the battlefields in the first stage of the game as reinforcements. The players then simultaneously allocate their remaining real-time resources, which can be randomized, in a decisive final stage. Our main contributions provide complete characterizations of the optimal reinforcement strategies and resulting equilibrium payoffs in these multi-stage General Lotto games. Interestingly, we determine that real-time resources are at least twice as effective as reinforcement resources when considering equilibrium payoffs.

翻译：战略决策往往跨越多个时间段，早期决策会影响竞争对手在后续阶段的成败。本文研究了一般洛托博弈中的这类动态过程——这类博弈模型描述了两名对手之间竞争性资源配置的机制。我们提出了一种两阶段模型：其中一名玩家在第一阶段可将预留资源作为强化资源战略性预分配至各战场；随后，双方在决定性的最终阶段同时分配各自剩余的可随机化实时资源。我们的主要贡献在于完整刻画了多阶段一般洛托博弈中最优强化策略及其对应的均衡收益。有趣的是，我们发现从均衡收益角度衡量，实时资源的效能至少是强化资源的两倍。