In the classical discrete Colonel Blotto game—introducedby Borel in 1921—two colonels simultaneously distributetheir troops across multiple battlefields. The winner of eachbattlefield is determined by a winner-take-all rule, independentlyof other battlefields. In the original formulation, eachcolonel’s goal is to win as many battlefields as possible. TheBlotto game and its extensions have been used in a widerange of applications from political campaign—exemplifiedby the U.S presidential election—to marketing campaign,from (innovative) technology competition to sports competition.Despite persistent efforts, efficient methods for findingthe optimal strategies in Blotto games have been elusivefor almost a century—due to exponential explosion inthe organic solution space—until Ahmadinejad, Dehghani,Hajiaghayi, Lucier, Mahini, and Seddighin developed thefirst polynomial-time algorithm for this fundamental gametheoreticalproblem in 2016. However, that breakthroughpolynomial-time solution has some structural limitation. Itapplies only to the case where troops are homogeneous withrespect to battlegruounds, as in Borel’s original formulation:For each battleground, the only factor that matters to the winner’spayoff is how many troops as opposed to which sets oftroops are opposing one another in that battleground.In this paper, we consider a more general setting of thetwo-player-multi-battleground game, in which multifacetedresources (troops) may have different contributions to differentbattlegrounds. In the case of U.S presidential campaign,for example, one may interpret this as different typesofmore »
This content will become publicly available on May 11, 2023
Fast and Simple Solutions of Blotto Games
In the Colonel Blotto game, which was initially introduced by Borel in 1921, two colonels simultaneously distribute their troops across different battlefields. The winner of each battlefield is determined independently by a winner-takes-all rule. The ultimate payoff for each colonel is the number of battlefields won. The Colonel Blotto game is commonly used for analyzing a wide range of applications from the U.S. Presidential election to innovative technology competitions to advertising, sports, and politics. There are persistent efforts to find the optimal strategies for the Colonel Blotto game. However, the first polynomial-time algorithm for that has very recently been provided by Ahmadinejad, Dehghani, Hajiaghayi, Lucier, Mahini, and Seddighin. Their algorithm consists of an exponential size linear program (LP), which they solve using the ellipsoid method. Because of the use of the ellipsoid method, despite its significant theoretical importance, this algorithm is highly impractical. In general, even the simplex method (despite its exponential running time in practice) performs better than the ellipsoid method in practice. In this paper, we provide the first polynomial-size LP formulation of the optimal strategies for the Colonel Blotto game using linear extension techniques. Roughly speaking, we consider the natural representation of the strategy space polytope and more »
- Award ID(s):
- 2114269
- Publication Date:
- NSF-PAR ID:
- 10325844
- Journal Name:
- Operations Research
- ISSN:
- 0030-364X
- Sponsoring Org:
- National Science Foundation
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