We leverage a new algorithm for numerically solving Colonel Blotto games to gain insight into a version of the game where players have different types of resources. Specifically, the winner of a battlefield is a function of a multi-dimensional allocation vector of each player. Our main focus is on the potential benefits of fractionation, which we define as the degree to which a player can quantize its resources. When players only have one type of resource, we show that the benefits to fractionation are in general, greatest in resource poor environments and against aggregated adversaries. We then extend the model to include random dropout and show that fractionation increases robustness to failure in resource poor environments but not resource rich environments. Finally, we show that when players have different types of resources, the benefits of fractionation are no longer mitigated by an increase in the total force size. Since many real-world resource allocation problems are multi-dimensional, our results illustrate the importance of analyzing multi-resource Blotto games in tandem with the traditional specification.
Grana, Justin, Jonathan Lamb, and Nicholas A. O'Donoughue, The Benefits of Fractionation in Competitive Resource Allocation. Santa Monica, CA: RAND Corporation, 2020. https://www.rand.org/pubs/working_papers/WR1329.html.
Grana, Justin, Jonathan Lamb, and Nicholas A. O'Donoughue, The Benefits of Fractionation in Competitive Resource Allocation, Santa Monica, Calif.: RAND Corporation, WR-1329-OSD, 2020. As of January 12, 2022: https://www.rand.org/pubs/working_papers/WR1329.html