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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 35 / No. 6: AAAI-21 Technical Tracks 6

Computational Analyses of the Electoral College: Campaigning Is Hard But Approximately Manageable

February 1, 2023

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Authors

Sina Dehghani

Institute for Research in Fundamental Sciences


Hamed Saleh

University of Maryland


Saeed Seddighin

Toyota Technological Institute


Shang-Hua Teng

University of Southern California


DOI:

10.1609/aaai.v35i6.16668


Abstract:

In the classical discrete Colonel Blotto game—introduced by Borel in 1921—two colonels simultaneously distribute their troops across multiple battlefields. The winner of each battlefield is determined by a winner-take-all rule, independently of other battlefields. In the original formulation, each colonel’s goal is to win as many battlefields as possible. The Blotto game and its extensions have been used in a wide range of applications from political campaign—exemplified by the U.S presidential election—to marketing campaign, from (innovative) technology competition to sports competition. Despite persistent efforts, efficient methods for finding the optimal strategies in Blotto games have been elusive for almost a century—due to exponential explosion in the organic solution space—until Ahmadinejad, Dehghani, Hajiaghayi, Lucier, Mahini, and Seddighin developed the first polynomial-time algorithm for this fundamental gametheoretical problem in 2016. However, that breakthrough polynomial-time solution has some structural limitation. It applies only to the case where troops are homogeneous with respect to battlegruounds, as in Borel’s original formulation: For each battleground, the only factor that matters to the winner’s payoff is how many troops as opposed to which sets of troops are opposing one another in that battleground. In this paper, we consider a more general setting of the two-player-multi-battleground game, in which multifaceted resources (troops) may have different contributions to different battlegrounds. In the case of U.S presidential campaign, for example, one may interpret this as different types of resources—human, financial, political—that teams can invest in each state. We provide a complexity-theoretical evidence that, in contrast to Borel’s homogeneous setting, finding optimal strategies in multifaceted Colonel Blotto games is intractable. We complement this complexity result with a polynomial-time algorithm that finds approximately optimal strategies with provable guarantees. We also study a further generalization when two competitors do not have zerosum/ constant-sum payoffs. We show that optimal strategies in these two-player-multi-battleground games are as hard to compute and approximate as Nash equilibria in general noncooperative games and economic equilibria in exchange markets.

Topics: AAAI

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HOW TO CITE:

Sina Dehghani||Hamed Saleh||Saeed Seddighin||Shang-Hua Teng Computational Analyses of the Electoral College: Campaigning Is Hard But Approximately Manageable Proceedings of the AAAI Conference on Artificial Intelligence (2021) 5294-5302.

Sina Dehghani||Hamed Saleh||Saeed Seddighin||Shang-Hua Teng Computational Analyses of the Electoral College: Campaigning Is Hard But Approximately Manageable AAAI 2021, 5294-5302.

Sina Dehghani||Hamed Saleh||Saeed Seddighin||Shang-Hua Teng (2021). Computational Analyses of the Electoral College: Campaigning Is Hard But Approximately Manageable. Proceedings of the AAAI Conference on Artificial Intelligence, 5294-5302.

Sina Dehghani||Hamed Saleh||Saeed Seddighin||Shang-Hua Teng. Computational Analyses of the Electoral College: Campaigning Is Hard But Approximately Manageable. Proceedings of the AAAI Conference on Artificial Intelligence 2021 p.5294-5302.

Sina Dehghani||Hamed Saleh||Saeed Seddighin||Shang-Hua Teng. 2021. Computational Analyses of the Electoral College: Campaigning Is Hard But Approximately Manageable. "Proceedings of the AAAI Conference on Artificial Intelligence". 5294-5302.

Sina Dehghani||Hamed Saleh||Saeed Seddighin||Shang-Hua Teng. (2021) "Computational Analyses of the Electoral College: Campaigning Is Hard But Approximately Manageable", Proceedings of the AAAI Conference on Artificial Intelligence, p.5294-5302

Sina Dehghani||Hamed Saleh||Saeed Seddighin||Shang-Hua Teng, "Computational Analyses of the Electoral College: Campaigning Is Hard But Approximately Manageable", AAAI, p.5294-5302, 2021.

Sina Dehghani||Hamed Saleh||Saeed Seddighin||Shang-Hua Teng. "Computational Analyses of the Electoral College: Campaigning Is Hard But Approximately Manageable". Proceedings of the AAAI Conference on Artificial Intelligence, 2021, p.5294-5302.

Sina Dehghani||Hamed Saleh||Saeed Seddighin||Shang-Hua Teng. "Computational Analyses of the Electoral College: Campaigning Is Hard But Approximately Manageable". Proceedings of the AAAI Conference on Artificial Intelligence, (2021): 5294-5302.

Sina Dehghani||Hamed Saleh||Saeed Seddighin||Shang-Hua Teng. Computational Analyses of the Electoral College: Campaigning Is Hard But Approximately Manageable. AAAI[Internet]. 2021[cited 2023]; 5294-5302.


ISSN: 2374-3468


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Copyright 2022, Association for the Advancement of
Artificial Intelligence 1900 Embarcadero Road, Suite
101, Palo Alto, California 94303 All Rights Reserved

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