Reinforcement Strategies in General Lotto Games

Abstract

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.