Problem
Research questions and friction points this paper is trying to address.
resource allocation
General Lotto games
security values
operational constraints
adversarial settings
Beyond Arbitrary Allocations: Security Values in Constrained General Lotto Games
🤖 AI Summary
This work proposes a novel constrained General Lotto game model for multi-battlefield contest scenarios where one player is restricted to allocate resources to only a single battlefield. For the first time, such a single-battlefield allocation constraint is formally incorporated into the General Lotto framework. By leveraging security-level analysis, probabilistic modeling, and optimization techniques from game theory, the study derives tight upper and lower bounds on the constrained player’s security value and characterizes equilibrium behavior within the restricted strategy space. The results demonstrate how operational constraints fundamentally reshape competitive strategies, quantify the performance cost imposed by allocation restrictions on optimal play and guaranteed outcomes, and bridge the gap between idealized theoretical models and real-world feasibility constraints—thereby offering new theoretical foundations and decision-making insights for adversarial resource allocation problems.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Constrained General Lotto
Security Values
Resource Allocation
Strategic Constraints
Game Theory
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