Stackelberg vs Nash in the Lottery Colonel Blotto Game
<|reference_start|>Stackelberg vs Nash in the Lottery Colonel Blotto Game: 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, business 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's utility can be unbounded compared to its utility in 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.<|reference_end|>
@article{liu2024stackelberg,
    title={Stackelberg vs. Nash in the Lottery Colonel Blotto Game},
    author={Yan Liu, Bonan Ni, Weiran Shen, Zihe Wang, Jie Zhang},
    journal={arXiv preprint arXiv:2410.07690},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.07690},
    primaryClass={cs.GT}
}