Beyond Arbitrary Allocations: Security Values in Constrained General Lotto Games

Abstract

Resource allocation problems across multiple contests are ubiquitous in adversarial settings, from military operations to market competition. While Colonel Blotto and General Lotto games have provided valuable theoretical foundations for such problems, their equilibrium characterizations typically permit resources to be arbitrarily allocated across all contests -- a flexibility that rarely aligns with practical constraints. This paper introduces a novel constrained variant of the General Lotto game where one player is restricted to allocating resources to only a single contest. In this model we provide lower and upper bounds on the security values for this constrained player, quantifying how the inability to distribute resources across multiple contests fundamentally changes optimal strategic behavior and performance guarantees. These findings contribute to a broader understanding of how operational constraints shape strategic outcomes in competitive resource allocation, with implications for decision-makers facing similar constraints in practice.