The Benefits of Fractionation in Competitive Resource Allocation

by Justin Grana, Jonathan Lamb, Nicholas A. O'Donoughue

Full Document

FormatFile SizeNotes
PDF file 0.6 MB

Use Adobe Acrobat Reader version 10 or higher for the best experience.

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.

This research was sponsored by the Defense Advanced Research Projects Agency's Strategic Technology Office and conducted within the Acquisition and Technology Policy Center of the RAND National Defense Research Institute, a federally funded research and development center sponsored by the Office of the Secretary of Defense, the Joint Staff, the Unified Combatant Commands, the Navy, the Marine Corps, the defense agencies, and the defense Intelligence Community.

This report is part of the RAND Corporation Working paper series. RAND working papers are intended to share researchers' latest findings and to solicit informal peer review. They have been approved for circulation by RAND but may not have been formally edited or peer reviewed.

Permission is given to duplicate this electronic document for personal use only, as long as it is unaltered and complete. Copies may not be duplicated for commercial purposes. Unauthorized posting of RAND PDFs to a non-RAND Web site is prohibited. RAND PDFs are protected under copyright law. For information on reprint and linking permissions, please visit the RAND Permissions page.

The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.