Computer Science > Computer Science and Game Theory
[Submitted on 10 Oct 2024 (v1), last revised 15 Oct 2024 (this version, v2)]
Title:Stackelberg vs. Nash in the Lottery Colonel Blotto Game
View PDFAbstract:Resource competition problems are often modeled using Colonel Blotto games. However, Colonel Blotto games only simulate scenarios where players act simultaneously. In many real-life scenarios, competition is sequential, such as cybersecurity, cloud services, Web investments, and more. To model such sequential competition, we model the Lottery Colonel Blotto game as a Stackelberg game. We solve the Stackelberg equilibrium in the Lottery Colonel Blotto game in which the first mover's strategy is actually a solution to a bi-level optimization problem. We develop a constructive method that allows for a series of game reductions. This method enables us to compute the leader's optimal commitment strategy in a polynomial number of iterations. Furthermore, we identify the conditions under which the Stackelberg equilibrium aligns with the Nash equilibria. Finally, we show that by making the optimal first move, the leader can improve utility by an infinite factor compared to its utility in the Nash equilibria. We find that the player with a smaller budget has a greater incentive to become the leader in the game. Surprisingly, even when the leader adopts the optimal commitment strategy, the follower's utility may improve compared to that in Nash equilibria.
Submission history
From: Yan Liu [view email][v1] Thu, 10 Oct 2024 08:00:22 UTC (46 KB)
[v2] Tue, 15 Oct 2024 11:55:49 UTC (46 KB)
References & Citations
Bibliographic and Citation Tools
Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)
Demos
Recommenders and Search Tools
Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.