Optimal competitive resource assignment in two-stage Colonel Blotto game with Lanchester-type attrition

In strategic decision-making tasks, determining how to assign limited costly resource towards the defender and the attacker is a central problem. However, it is hard for pre-allocated resource assignment to adapt to dynamic fighting scenarios, and exists situations where the scenario and rule of the Colonel Blotto (CB) game are too restrictive in real world. To address these issues, a support stage is added as supplementary for pre-allocated results, in which a novel two-stage competitive resource assignment problem is formulated based on CB game and stochastic Lanchester equation (SLE). Further, the force attrition in these two stages is formulated as a stochastic progress to consider the complex fighting progress, including the case that the player with fewer resources defeats the player with more resources and wins the battlefield. For solving this two-stage resource assignment problem, nested solving and noregret learning are proposed to search the optimal resource assignment strategies. Numerical experiments are taken to analyze the effectiveness of the proposed model and study the assignment strategies in various cases.