# The Multiplayer Colonel Blotto Game

@article{BoixAdser2020TheMC, title={The Multiplayer Colonel Blotto Game}, author={Enric Boix-Adser{\`a} and Benjamin L. Edelman and Siddhartha V. Jayanti}, journal={Proceedings of the 21st ACM Conference on Economics and Computation}, year={2020} }

We initiate the study of the natural multiplayer generalization of the classic continuous Colonel Blotto game.The two-player Blotto game, introduced by Borel as a model of resource competition across nsimultaneous fronts, has been studied extensively for a century and seen numerous applications throughout the social sciences. Our work defines the multiplayer Colonel Blotto gameand derives Nash equilibria for various settings of k(number of players) and n(number of battlefields)---in particular…

## 9 Citations

Nash Equilibria of The Multiplayer Colonel Blotto Game on Arbitrary Measure Spaces

- Computer ScienceArXiv
- 2021

The classical theory is extended to study multiplayer Blotto games over arbitrary measurable battlegrounds, an algorithm is provided to efficiently sample equilibria of symmetric “equipartionable” Generalized Blottogames, and the symmetric fair equilibrio of the Blotto game over the unit interval is characterized.

Colonel Blotto Games with Favoritism: Competitions with Pre-allocations and Asymmetric Effectiveness

- Computer ScienceEC
- 2021

It is proved the existence of a set of optimal univariate distributions---which serve as candidate marginals for an equilibrium---of the Colonel Blotto game with favoritism and an algorithm is proposed to efficiently compute an approximation of the proposed optimalunivariate distributions with arbitrarily small error.

A General Lotto game with asymmetric budget uncertainty

- Computer Science, EngineeringArXiv
- 2021

It is found the optimal randomized assignment strategy can actually improve the commander’s payoff two-fold when compared to optimal deterministic assignments, and four-fold in settings where the commander also pays a per-unit cost for resources.

Comments on Quantization and experimental realization of the Colonel Blotto game

- Computer ScienceQuantum Inf. Process.
- 2020

This note focuses on an exemplary case where the quantum payoff does not agree with the classical payoff at classical limits, i.e., when both players play classical strategies.

Strategically revealing intentions in General Lotto games

- Computer Science, EngineeringArXiv
- 2021

Interestingly, this paper highlights many scenarios where strategically revealing intentions can actually significantly improve one’s payoff, which runs contrary to the conventional wisdom that randomness should be a central component of decision-making in adversarial environments.

Quantum Multiplayer Colonel Blotto Game.

- Computer Science, Physics
- 2020

It is found that players with access to the quantum strategies has a advantage over the classical ones and the payoff is invariant under the order of the strategies.

An Efficient Approximation Algorithm for the Colonel Blotto Game

- Computer Science
- 2022

In the storied Colonel Blotto game, two colonels allocate a and b troops, respectively, to k distinct battlefields. A colonel wins a battle if they assign more troops to that particular battle, and…

Sample-based Approximation of Nash in Large Many-Player Games via Gradient Descent

- Computer ScienceArXiv
- 2021

The lack of local convergence guarantees for biased gradient descent prevents guaranteed convergence to Nash, however, it is demonstrated the ability of this approach to approximate a unique Nash equilibrium in normal-form games with as many as seven players and twenty one actions that are orders of magnitude larger than those possible with prior algorithms.

Approximate Equilibria in Generalized Colonel Blotto and Generalized Lottery Blotto Games

- Computer Science
- 2019

A simply-constructed class of strategies are proposed and it is proved that they are approximate equilibria of the Generalized Colonel Blotto game; moreover, the approximation error is characterized according to the game's parameters.

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