A Genetic Algorithm approach to Asymmetrical Blotto Games with Heterogeneous Valuations

TL;DR

This paper introduces a genetic algorithm to solve asymmetrical Blotto games, revealing strategic behaviors like resource concentration and battlefield valuation effects, aligning with empirical observations.

Contribution

It develops a novel genetic algorithm approach to analyze asymmetrical Blotto games, capturing complex strategies and equilibria with heterogeneous valuations.

Findings

Converges to symmetric Nash equilibrium in symmetric cases

Emergence of 'guerilla warfare' strategies under resource asymmetry

Counter-strategies arise with heterogeneous battlefield valuations

Abstract

Blotto Games are a popular model of multi-dimensional strategic resource allocation. Two players allocate resources in different battlefields in an auction setting. While competition with equal budgets is well understood, little is known about strategic behavior under asymmetry of resources. We introduce a genetic algorithm, a search heuristic inspired from biological evolution, interpreted as social learning, to solve this problem. Most performant strategies are combined to create more performant strategies. Mutations allow the algorithm to efficiently scan the space of possible strategies, and consider a wide diversity of deviations. We show that our genetic algorithm converges to the analytical Nash equilibrium of the symmetric Blotto game. We present the solution concept it provides for asymmetrical Blotto games. It notably sees the emergence of "guerilla warfare" strategies, consistent with empirical and experimental findings. The player with less resources learns to concentrate its resources to compensate for the asymmetry of competition. When players value battlefields heterogeneously, counter strategies and bidding focus is obtained in equilibrium. These features are consistent with empirical and experimental findings, and provide a learning foundation for their existence.