A Genetic Algorithm approach to Asymmetrical Blotto Games with Heterogeneous Valuations
This provides a learning-based solution for modeling competition under resource asymmetry, relevant for game theory and strategic decision-making, though it is incremental as it applies an existing heuristic to a less understood problem.
The paper tackled the problem of strategic resource allocation in asymmetrical Blotto games with heterogeneous valuations by introducing a genetic algorithm, which converges to the Nash equilibrium in symmetric cases and reveals strategies like 'guerilla warfare' and bidding focus in asymmetrical scenarios, consistent with empirical findings.
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.