Journal articles: 'Colonel Blotto Game'

1

Roberson, Brian. "The Colonel Blotto game." Economic Theory 29, no. 1 (January 18, 2006): 1–24. http://dx.doi.org/10.1007/s00199-005-0071-5.

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Boix-Adserà, Enric, Benjamin L. Edelman, and Siddhartha Jayanti. "The multiplayer Colonel Blotto game." Games and Economic Behavior 129 (September 2021): 15–31. http://dx.doi.org/10.1016/j.geb.2021.05.002.

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Rinott, Yosef, Marco Scarsini, and Yaming Yu. "A Colonel Blotto Gladiator Game." Mathematics of Operations Research 37, no. 4 (November 2012): 574–90. http://dx.doi.org/10.1287/moor.1120.0550.

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4

Homburg, Stefan. "Colonel Blotto und seine ökonomischen Anwendungen." Perspektiven der Wirtschaftspolitik 12, no. 1 (February 2011): 1–11. http://dx.doi.org/10.1111/j.1468-2516.2010.00347.x.

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AbstractRedistributional issues are important in contemporary welfare states. These issues cannot be analyzed using the median voter theorem because preferences fail singlepeakedness: Collective preferences are intransitive, giving rise to cyclical preferences. A suitable instrument for analyzing redistributional issues is the Colonel Blotto game. This game is older than the more familiar prisoner’s dilemma, but it has been solved only recently. The article introduces the Colonel Blotto Game as well as the general structure of its solutions. Thereafter, the game’s logic is illustrated using several policy examples. The two most fascinating results state that, in a political contest, it is never optimal to use pure strategies, and that the political process itself induces remarkable inequalities.

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Roberson, Brian, and Dmitriy Kvasov. "The non-constant-sum Colonel Blotto game." Economic Theory 51, no. 2 (October 28, 2011): 397–433. http://dx.doi.org/10.1007/s00199-011-0673-z.

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Dehghani, Sina, Hamed Saleh, Saeed Seddighin, and Shang-Hua Teng. "Computational Analyses of the Electoral College: Campaigning Is Hard But Approximately Manageable." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 6 (May 18, 2021): 5294–302. http://dx.doi.org/10.1609/aaai.v35i6.16668.

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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.

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Kharlamov, V. V. "On Asymptotic Strategies in the Stochastic Colonel Blotto Game." Theory of Probability & Its Applications 67, no. 2 (August 2022): 318–26. http://dx.doi.org/10.1137/s0040585x97t990952.

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HAUSKEN, KJELL. "ON THE IMPOSSIBILITY OF DETERRENCE IN SEQUENTIAL COLONEL BLOTTO GAMES." International Game Theory Review 14, no. 02 (June 2012): 1250011. http://dx.doi.org/10.1142/s0219198912500119.

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A sequential Colonel Blotto and rent seeking game with fixed and variable resources is analyzed. With fixed resources, which is the assumption in Colonel Blotto games, we show for the common ratio form contest success function that the second mover is never deterred. This stands in contrast to Powell's (Games and Economic Behavior67(2), 611–615) finding where the second mover can be deterred. With variable resources both players exert efforts in both sequential and simultaneous games, whereas fixed resources cause characteristics of all battlefields or rents to impact efforts for each battlefield. With variable resources only characteristics of a given battlefield impact efforts are to win that battlefield because of independence across battlefields. Fixed resources impact efforts and hence differences in unit effort costs are less important. In contrast, variable resources cause differences in unit effort costs to be important. The societal implication is that resource constrained opponents can be expected to engage in warfare, whereas an advantaged player with no resource constraints can prevent warfare.

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Hernández, Damián G., and Damián H. Zanette. "Evolutionary Dynamics of Resource Allocation in the Colonel Blotto Game." Journal of Statistical Physics 151, no. 3-4 (December 14, 2012): 623–36. http://dx.doi.org/10.1007/s10955-012-0659-7.

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Zhang, Long, Yao Wang, and Zhu Han. "Safeguarding UAV-Enabled Wireless Power Transfer Against Aerial Eavesdropper: A Colonel Blotto Game." IEEE Wireless Communications Letters 11, no. 3 (March 2022): 503–7. http://dx.doi.org/10.1109/lwc.2021.3133891.

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Arad, Ayala, and Ariel Rubinstein. "Multi-dimensional iterative reasoning in action: The case of the Colonel Blotto game." Journal of Economic Behavior & Organization 84, no. 2 (November 2012): 571–85. http://dx.doi.org/10.1016/j.jebo.2012.09.004.

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12

Kovenock, Dan, and David Rojo Arjona. "A full characterization of best-response functions in the lottery Colonel Blotto game." Economics Letters 182 (September 2019): 33–36. http://dx.doi.org/10.1016/j.econlet.2019.05.040.

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Min, Minghui, Liang Xiao, Caixia Xie, Mohammad Hajimirsadeghi, and Narayan B. Mandayam. "Defense Against Advanced Persistent Threats in Dynamic Cloud Storage: A Colonel Blotto Game Approach." IEEE Internet of Things Journal 5, no. 6 (December 2018): 4250–61. http://dx.doi.org/10.1109/jiot.2018.2844878.

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14

Adam, Lukáš, Rostislav Horčík, Tomáš Kasl, and Tomáš Kroupa. "Double Oracle Algorithm for Computing Equilibria in Continuous Games." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 6 (May 18, 2021): 5070–77. http://dx.doi.org/10.1609/aaai.v35i6.16641.

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Many efficient algorithms have been designed to recover Nash equilibria of various classes of finite games. Special classes of continuous games with infinite strategy spaces, such as polynomial games, can be solved by semidefinite programming. In general, however, continuous games are not directly amenable to computational procedures. In this contribution, we develop an iterative strategy generation technique for finding a Nash equilibrium in a whole class of continuous two-person zero-sum games with compact strategy sets. The procedure, which is called the double oracle algorithm, has been successfully applied to large finite games in the past. We prove the convergence of the double oracle algorithm to a Nash equilibrium. Moreover, the algorithm is guaranteed to recover an approximate equilibrium in finitely-many steps. Our numerical experiments show that it outperforms fictitious play on several examples of games appearing in the literature. In particular, we provide a detailed analysis of experiments with a version of the continuous Colonel Blotto game.

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Zhuang, Hejun. "Modeling Strategic Location Choices for Disadvantaged Firms." International Business Research 11, no. 10 (September 20, 2018): 59. http://dx.doi.org/10.5539/ibr.v11n10p59.

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This paper models how a firm’s capability relative to that of the other firm affects his location choice in the marketplace. Weaker firms strategically avoid head-to-head competition with stronger ones. When the capability gap is small, weaker firms randomly visit the core market of competitors (the “dodge” strategy). By doing so, they can trigger competitors to leave the demands of boundary markets in order to defend their core markets. When the capability gap is medium, they focus their resources on niches to fight for survival (the “niche” strategy). These strategies differ from those of stronger firms, which defend on core markets when the capability gap is small and build new markets when the capability gap becomes larger. Results show that those location choices can be understood using game theoretical models – the Hotelling model and the Colonel Blotto game. The paper’s results also explain the empirical observation that small businesses are more likely than large firms to make radical investments in R&D.

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Tan, C. K., S. W. Tan, and T. C. Chuah. "Fair subcarrier and power allocation for multiuser orthogonal frequency-division multiple access cognitive radio networks using a Colonel Blotto game." IET Communications 5, no. 11 (July 22, 2011): 1607–18. http://dx.doi.org/10.1049/iet-com.2010.1021.

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Ji, Xiang, Wanpeng Zhang, Fengtao Xiang, Weilin Yuan, and Jing Chen. "A Swarm Confrontation Method Based on Lanchester Law and Nash Equilibrium." Electronics 11, no. 6 (March 14, 2022): 896. http://dx.doi.org/10.3390/electronics11060896.

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In this paper, more efficient allocation of forces is analyzed in the future air confrontation among unmanned aerial vehicle swarms. A novel method is proposed for swarm confrontation based on the Lanchester law and Nash equilibrium. Due to the huge number of unmanned aerial vehicles, it is not beneficial to deploy UAV forces in swarm confrontation. Moreover, unmanned aerial vehicles do not have high maneuverability in collaboration. Therefore, we propose to divide the swarms of unmanned aerial vehicles into groups, so that swarms of both sides can fight in different battlefields, which could be considered as a Colonel Blotto Game. Inspired by the double oracle algorithm, a Nash equilibrium solving method is proposed to searched for the best force allocation of the swarm confrontation. In addition, this paper proposes the concept of the boundary contact rate and carries out quantitative numerical analysis with the Lanchester law. Experiments reveal the relationship between the boundary contact rate and the optimal strategy of swarm confrontation, which could guide the force allocation in future swarm confrontation. Furthermore, the effectiveness of the division method and the double oracle-based equilibrium solving algorithm proposed in this paper is verified.

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18

Hart, Sergiu. "Discrete Colonel Blotto and General Lotto games." International Journal of Game Theory 36, no. 3-4 (October 12, 2007): 441–60. http://dx.doi.org/10.1007/s00182-007-0099-9.

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19

Chowdhury, Subhasish M., Dan Kovenock, and Roman M. Sheremeta. "An experimental investigation of Colonel Blotto games." Economic Theory 52, no. 3 (October 20, 2011): 833–61. http://dx.doi.org/10.1007/s00199-011-0670-2.

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Guan, Sanghai, Jingjing Wang, Haipeng Yao, Chunxiao Jiang, Zhu Han, and Yong Ren. "Colonel Blotto Games in Network Systems: Models, Strategies, and Applications." IEEE Transactions on Network Science and Engineering 7, no. 2 (April 1, 2020): 637–49. http://dx.doi.org/10.1109/tnse.2019.2904530.

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KOVENOCK, DAN, and BRIAN ROBERSON. "Coalitional Colonel Blotto Games with Application to the Economics of Alliances." Journal of Public Economic Theory 14, no. 4 (July 24, 2012): 653–76. http://dx.doi.org/10.1111/j.1467-9779.2012.01556.x.

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22

Hortala-Vallve, Rafael, and Aniol Llorente-Saguer. "Pure strategy Nash equilibria in non-zero sum colonel Blotto games." International Journal of Game Theory 41, no. 2 (June 18, 2011): 331–43. http://dx.doi.org/10.1007/s00182-011-0288-4.

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23

Ewerhart, Christian, and Dan Kovenock. "A class of N-player Colonel Blotto games with multidimensional private information." Operations Research Letters 49, no. 3 (May 2021): 418–25. http://dx.doi.org/10.1016/j.orl.2021.03.010.

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Vu, Dong Quan, Patrick Loiseau, Alonso Silva, and Long Tran-Thanh. "Path Planning Problems with Side Observations—When Colonels Play Hide-and-Seek." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 02 (April 3, 2020): 2252–59. http://dx.doi.org/10.1609/aaai.v34i02.5602.

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Resource allocation games such as the famous Colonel Blotto (CB) and Hide-and-Seek (HS) games are often used to model a large variety of practical problems, but only in their one-shot versions. Indeed, due to their extremely large strategy space, it remains an open question how one can efficiently learn in these games. In this work, we show that the online CB and HS games can be cast as path planning problems with side-observations (SOPPP): at each stage, a learner chooses a path on a directed acyclic graph and suffers the sum of losses that are adversarially assigned to the corresponding edges; and she then receives semi-bandit feedback with side-observations (i.e., she observes the losses on the chosen edges plus some others). We propose a novel algorithm, Exp3-OE, the first-of-its-kind with guaranteed efficient running time for SOPPP without requiring any auxiliary oracle. We provide an expected-regret bound of Exp3-OE in SOPPP matching the order of the best benchmark in the literature. Moreover, we introduce additional assumptions on the observability model under which we can further improve the regret bounds of Exp3-OE. We illustrate the benefit of using Exp3-OE in SOPPP by applying it to the online CB and HS games.

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Behnezhad, Soheil, Sina Dehghani, Mahsa Derakhshan, MohammadTaghi Hajiaghayi, and Saeed Seddighin. "Faster and Simpler Algorithm for Optimal Strategies of Blotto Game." Proceedings of the AAAI Conference on Artificial Intelligence 31, no. 1 (February 10, 2017). http://dx.doi.org/10.1609/aaai.v31i1.10620.

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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-take-all rule. The ultimate payoff of each colonel is the number of battleﬁelds he wins. This game is commonly used for analyzing a wide range of applications such as the U.S presidential election, innovative technology competitions, advertisements, etc. There have been persistent efforts for ﬁnding the optimal strategies for the Colonel Blotto game. After almost a century Ahmadinejad, Dehghani, Hajiaghayi, Lucier, Mahini, and Seddighin provided a poly-time algorithm for ﬁnding the optimal strategies. They ﬁrst model the problem by a Linear Program (LP) with exponential number of constraints and use Ellipsoid method to solve it. However, despite the theoretical importance of their algorithm, it ishighly impractical. In general, even Simplex method (despite its exponential running-time) performs better than Ellipsoid method in practice. In this paper, we provide the ﬁrst polynomial-size LP formulation of the optimal strategies for the Colonel Blotto game. We use linear extension techniques. Roughly speaking, we project the strategy space polytope to a higher dimensional space, which results in a lower number of facets for the polytope.We use this polynomial-size LP to provide a novel, simpler and signiﬁcantly faster algorithm for ﬁnding the optimal strategies for the Colonel Blotto game. We further show this representation is asymptotically tight in terms of the number of constraints. We also extend our approach to multi-dimensional Colonel Blotto games, and implement our algorithm to observe interesting properties of Colonel Blotto; for example, we observe the behavior of players in the discrete model is very similar to the previously studied continuous model.

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Rinott, Yosef, Marco Scarsini, and Yaming Yu. "A Colonel Blotto Gladiator Game." SSRN Electronic Journal, 2012. http://dx.doi.org/10.2139/ssrn.2033887.

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Behnezhad, Soheil, Sina Dehghani, Mahsa Derakhshan, Mohammedtaghi Hajiaghayi, and Saeed Seddighin. "Fast and Simple Solutions of Blotto Games." Operations Research, March 18, 2022. http://dx.doi.org/10.1287/opre.2022.2261.

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The Colonel Blotto game (initially introduced by Borel in 1921) is commonly used for analyzing a wide range of applications from the U.S.Ppresidential election to innovative technology competitions to advertising, sports, and politics. After around a century Ahmadinejad et al. provided the first polynomial-time algorithm for computing the Nash equilibria in Colonel Blotto games. However, their algorithm consists of an exponential-size LP solved by the ellipsoid method, which is highly impractical. In “Fast and Simple Solutions of Blotto Games,” Behnezhad, Dehghani, Derakhshan, Hajighayi, and Seddighin provide the first polynomial-size LP formulation of the optimal strategies for the Colonel Blotto game using linear extension techniques. They use this polynomial-size LP to provide a simpler and significantly faster algorithm for finding optimal strategies of the Colonel Blotto game. They further show this representation is asymptotically tight, which means there exists no other linear representation of the strategy space with fewer constraints.

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28

Roberson, Brian, and Dmitriy Kvasov. "The Non-Constant-Sum Colonel Blotto Game." SSRN Electronic Journal, 2008. http://dx.doi.org/10.2139/ssrn.1261803.

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Solomon, Adam. "Symmetric Equilibrium in a Sequential Colonel Blotto Game." SSRN Electronic Journal, 2018. http://dx.doi.org/10.2139/ssrn.3095105.

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30

Roberson, Brian, and Oz Shy. "Costly force relocation in the Colonel Blotto game." Economic Theory Bulletin, August 27, 2020. http://dx.doi.org/10.1007/s40505-020-00192-7.

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31

Baba, Yumiko. "A Note on a Comparison of Simultaneous and Sequential Colonel Blotto Games." Peace Economics, Peace Science and Public Policy 18, no. 3 (December 13, 2012). http://dx.doi.org/10.1515/peps-2012-0007.

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Abstract Clark and Konrad (2007) introduce the weakest link against the best shot property to the Colonel Blotto game where the defendant has to win all the battle fields while the attacker only needs to win at least one battlefield. They characterize the Nash equilibrium assuming that the attacker attacks all the battlefields simultaneously. We construct a two stage model and endogenize the attacker’s attack pattern. We show that the attacker chooses a sequential attack pattern in the subgame perfect Nash equilibrium. Therefore, the game analyzed by Clark and Konrad (2007) is never realized. We also conducted experiments and found that the subjects’ behavior was inconsistent to theoretical predictions. Both players overinvested and the variances were large. In the simultaneous game, the attackers took a guerrira strategy at 30% of the time in which they invested only in one battlefield and the defenders took a surrender strategy at 11% of the time in which they invested nothing in the simultaneous game. Both players invested more in period 1 than in period 2 in the sequential game. Although all of these are inconsistent to the theoretical predictions, the winning probability of a game was consistent to the theoretical prediction in the simultaneous games, but it was lower than the theoretical prediction in the sequential games. We conclude that the subjects’ irrational behavior is mainly a rational response to his/ her opponent’s irrational behavior. Our model can explain terrorism, cyber terrorism, lobbying, and patent trolls and the huge gap between the theory and the experiments are important considering the significance of the problems.

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32

Maioli, A. C., M. H. M. Passos, W. F. Balthazar, C. E. R. Souza, J. A. O. Huguenin, and A. G. M. Schmidt. "Reply to “Comments on quantization of Colonel Blotto game”." Quantum Information Processing 19, no. 10 (October 2020). http://dx.doi.org/10.1007/s11128-020-02845-9.

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Maioli, A. C., M. H. M. Passos, W. F. Balthazar, C. E. R. Souza, J. A. O. Huguenin, and A. G. M. Schmidt. "Quantization and experimental realization of the Colonel Blotto game." Quantum Information Processing 18, no. 1 (November 22, 2018). http://dx.doi.org/10.1007/s11128-018-2113-5.

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34

Ferdowsi, Aidin, Walid Saad, and Narayan B. Mandayam. "Colonel Blotto Game for Sensor Protection in Interdependent Critical Infrastructure." IEEE Internet of Things Journal, 2020, 1. http://dx.doi.org/10.1109/jiot.2020.3020901.

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Naskar, Joydeep. "Comments on Quantization and experimental realization of the Colonel Blotto game." Quantum Information Processing 19, no. 10 (October 2020). http://dx.doi.org/10.1007/s11128-020-02734-1.

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36

Rehsmann, Daniel. "The Sumo coach problem." Review of Economic Design, November 4, 2022. http://dx.doi.org/10.1007/s10058-022-00316-4.

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AbstractWe address the optimal allocation of stochastically dependent resource bundles to a set of simultaneous contests. For this purpose, we study a modification of the Colonel Blotto Game called the Tennis Coach Problem. We devise a thoroughly probabilistic method of payoff representation and fully characterize equilibria in this class of games. We further formalize the idea of strategic team training in a comparative static setting. The problem applies to several distinct economic interactions but seems most prevalent in team sports with individual matches, for instance, in Tennis and Sumo.

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37

Tuyls, Karl, Julien Perolat, Marc Lanctot, Edward Hughes, Richard Everett, Joel Z. Leibo, Csaba Szepesvári, and Thore Graepel. "Bounds and dynamics for empirical game theoretic analysis." Autonomous Agents and Multi-Agent Systems 34, no. 1 (December 4, 2019). http://dx.doi.org/10.1007/s10458-019-09432-y.

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AbstractThis paper provides several theoretical results for empirical game theory. Specifically, we introduce bounds for empirical game theoretical analysis of complex multi-agent interactions. In doing so we provide insights in the empirical meta game showing that a Nash equilibrium of the estimated meta-game is an approximate Nash equilibrium of the true underlying meta-game. We investigate and show how many data samples are required to obtain a close enough approximation of the underlying game. Additionally, we extend the evolutionary dynamics analysis of meta-games using heuristic payoff tables (HPTs) to asymmetric games. The state-of-the-art has only considered evolutionary dynamics of symmetric HPTs in which agents have access to the same strategy sets and the payoff structure is symmetric, implying that agents are interchangeable. Finally, we carry out an empirical illustration of the generalised method in several domains, illustrating the theory and evolutionary dynamics of several versions of the AlphaGo algorithm (symmetric), the dynamics of the Colonel Blotto game played by human players on Facebook (symmetric), the dynamics of several teams of players in the capture the flag game (symmetric), and an example of a meta-game in Leduc Poker (asymmetric), generated by the policy-space response oracle multi-agent learning algorithm.

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Zhang, Long, Yao Wang, Minghui Min, Chao Guo, Vishal Sharma, and Zhu Han. "Privacy-Aware Laser Wireless Power Transfer for Aerial Multi-Access Edge Computing: A Colonel Blotto Game Approach." IEEE Internet of Things Journal, 2022, 1. http://dx.doi.org/10.1109/jiot.2022.3167052.

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Shy, Oz. "Colonel Blotto Games with Switching Costs." SSRN Electronic Journal, 2018. http://dx.doi.org/10.2139/ssrn.3306880.

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Shy, Oz. "Colonel Blotto Games with Reserved Troops." SSRN Electronic Journal, 2019. http://dx.doi.org/10.2139/ssrn.3316483.

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Liang, Dong, Yunlong Wang, Zhigang Cao, and Xiaoguang Yang. "Colonel Blotto Games with Two Battlefields." SSRN Electronic Journal, 2019. http://dx.doi.org/10.2139/ssrn.3318291.

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Chowdhury, Subhasish M., Daniel Kovenock, and Roman M. Sheremeta. "An Experimental Investigation of Colonel Blotto Games." SSRN Electronic Journal, 2009. http://dx.doi.org/10.2139/ssrn.1430284.

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Aspect, Leopold, and Christian Ewerhart. "Colonel Blotto Games with a Head Start." SSRN Electronic Journal, 2022. http://dx.doi.org/10.2139/ssrn.4204082.

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Li, Xinmi, and Jie Zheng. "Even-Split Strategy in Sequential Colonel Blotto Games." SSRN Electronic Journal, 2022. http://dx.doi.org/10.2139/ssrn.4089110.

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Li, Xinmi, and Jie Zheng. "Even-Split Strategy in Sequential Colonel Blotto Games." SSRN Electronic Journal, 2021. http://dx.doi.org/10.2139/ssrn.3947995.

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Kovenock, Daniel, and Brian Roberson. "Generalizations of the General Lotto and Colonel Blotto Games." SSRN Electronic Journal, 2015. http://dx.doi.org/10.2139/ssrn.2597975.

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Kovenock, Dan, and Brian Roberson. "Generalizations of the General Lotto and Colonel Blotto Games." SSRN Electronic Journal, 2015. http://dx.doi.org/10.2139/ssrn.2585352.

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Kovenock, Dan, and Brian Roberson. "Generalizations of the General Lotto and Colonel Blotto games." Economic Theory, June 20, 2020. http://dx.doi.org/10.1007/s00199-020-01272-2.

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ÇINAR, Yetkin, and Türkmen GÖKSEL. "An experimental analysis of Colonel Blotto Games under alternative environments." İktisat İşletme ve Finans 27, no. 312 (March 1, 2012). http://dx.doi.org/10.3848/iif.2012.312.3271.

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Li, Xinmi, and Jie Zheng. "Pure strategy Nash Equilibrium in 2-contestant generalized lottery Colonel Blotto games." Journal of Mathematical Economics, October 2022, 102771. http://dx.doi.org/10.1016/j.jmateco.2022.102771.

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Journal articles on the topic 'Colonel Blotto Game'

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