布洛托上校博弈模型及求解方法研究进展

doi:10.11896/jsjkx.230600011

Abstract

Abstract: Resource allocation under confrontation conditions is the core of most game decision problems.From fitting optimal solution to game equilibrium solution,resource allocation strategy solving based on game theory is a frontier topic in cognitive decision-making field.This paper summarizes and analyzes the Colonel Blotto game model and its solution method for adversarial resource allocation.Firstly,the differences between offline and online strategy learning,strategy game and related solution concepts,online optimization and regret value are briefly introduced.Secondly,six types of Colonel Blotto game models(continuous Blotto game,discrete Colonel Lotto game,generalized Colonel Blotto game,generalized Lotto Blotto game,generalized rule Colonel Lotto game and online discrete Colonel Lotto game).Then,this paper distinguishes 2 stages(offline and online) and 3 types of game scenarios(single,repeated,multi-stage),and analyzes the solution method of Colonel Blotto game.Finally,the future research frontiers are analyzed and prospected from four aspects:typical application exploration,generalized game model,game solving method and future research prospect.The main purpose is to give an overview of the current Colonel Blotto game,hoping to enlighten the research on resource allocation and game theory under confrontation condition.

Key words: Resource allocation, Colonel Blotto game, Approximate Nash equilibrium, Online convex optimization, Expected regret, High-probability regret

CLC Number:

TP181

LUO Junren, ZOU Mingwo, CHEN Shaofei, ZHANG Wanpeng, CHEN Jing. Research Progress on Colonel Blotto Game Models and Solving Methods[J].Computer Science, 2024, 51(1): 84-98.

References

[1]ZHAO J,YANG C.Graph Reinforcement Learning for Predictive Power Allocation to Mobile Users[EB/OL].(2022-03-08)(2022-11-01).https://arxiv.org/abs/2203.03906.
[2]PANIGRAHY N K,BASU P,NAIN P,et al.Resource Allocation in One-Dimensional Distributed Service Networks with Applications [J].Performance Evaluation.2020,142:102110.
[3]ABDALLAH M.Effects of Behavioral Decision-Making inGame-Theoretic Frameworks for Security Resource Allocation in Networked Systems [D].West Lafayette:Purdue University Graduate School,2022.
[4]JI X,ZHANG W,XIANG F,et al.A Swarm ConfrontationMethod Based on Lanchester Law and Nash Equilibrium [J].Electronics,2022,11(6):896.
[5]ZHANG X X,GE B F,TAN Y J.Multi-Attribute Game Theoretic Model for Resource Allocation in Military Attack Defense Application[J].Journal of National University of Defense Technology,2018,40(5):153-160.
[6]LIU B Y,YE X B,ZHOU C F,et al.Composite Mode On-Orbit Service Resource Allocation Based on Improved DQN[J].Acta Aeronautica et Astronautica Sinica,2020,41(5):9.
[7]YAN W,JINKUAN W,JINGHAO S.A Game-Theoretic Based Resource Allocation Strategy for Cloud Computing Services[J].Scientific Programming,2016,2016(Pt.2):1629893.1.
[8]MYERSON R B.Incentives to Cultivate Favored Minorities Under Alternative Electoral Systems [J].American Political Science Review,1993,87(4):856-869.
[9]JIANG Y J,KUANG K,WU F.Big Data Intelligence:From the Optimal Solution of Data Fitting to The Equilibrium Solution of Game Theory[J].CAAI Transactions on Intelligent Systems,2020,15(1):175-182.
[10]BOREL E.La Théorie Du Jeu Et Les Equations IntégralesaNoyau Symétrique [J].Comptes rendus de l’Académie des Sciences,1921,173(1304/1305/1306/1307/1308):58.
[11]NAKAYAMA M.The Dawn of Modern Theory of Games[J].Advances in Mathematical Economics,2006,9:73-97.
[12]GROSS O,WAGNER R.A Continuous Colonel Blotto Game [R].Rand Project Air Force Santa Monica Ca,1950.
[13]KOVENOCK D,ROBERSON B.Coalitional Colonel BlottoGames with Application to The Economics of Alliances [J].Journal of Public Economic Theory,2012,14(4):653-676.
[14]GRANA J,LAMB J,O’DONOUGHUE N A.Findings on Mosaic Warfare from a Colonel Blotto Game [R].Rand National Defense Research Inst Santa Monica Ca,2021.
[15]MORGENSTERN O,VON NEUMANN J.Theory of Gamesand Economic Behavior [M].Princeton University Press,1953.
[16]NASH J.Non-Cooperative Games [D].Annals of mathematics,1951:286-295.
[17]KALAI A,VEMPALA S.Efficient Algorithms for Online Decision Problems [J].Journal of Computer and System Sciences,2005,71(3):291-307.
[18]HANNAN J.Approximation to Bayes Risk in Repeated Play[J].Contributions to the Theory of Games,1957,3(2):97-139.
[19]ROBBINS H.Some Aspects of The Sequential Design of Experiments [J].Bulletin of the American Mathematical Society,1952,58(5):527-535.
[20]GYÖRGY A,LINDER T,LUGOSI G,et al.The On-Line Shortest Path Problem Under Partial Monitoring [J].Journal of Machine Learning Research,2007,8(10):2369-2403.
[21]KOCÁK T,NEU G,VALKO M,et al.Efficient Learning by Implicit Exploration in Bandit Problems with Side Observations [C]//Proceedings of the 27th International Conference on Neural Information Processing Systems.2014:613-621.
[22]BARTLETT P,DANI V,HAYES T,et al.High-ProbabilityRegret Bounds for Bandit Online Linear Optimization [C]//Proceedings of the 21st Annual Conference on Learning Theory-COLT.2008:335-342.
[23]LAI T L,ROBBINS H.Asymptotically Efficient Adaptive Allocation Rules [J].Advances in Applied Mathematics,1985,6(1):4-22.
[24]AUER P,CESA-BIANCHI N,FISCHER P.Finite-Time Analysis of The Multiarmed Bandit Problem [J].Machine Learning,2002,47(2):235-256.
[25]BUBECK S,CESA-BIANCHI N.Regret Analysis of Stochastic and Non-Stochastic Multi-Armed Bandit Problems [J].Foundations and Trends© in Machine Learning,2012,5(1):1-122.
[26]GARIVIER A,CAPPÉ O.The KL-UCB Algorithm for Bounded Stochastic Bandits and Beyond [C]//Proceedings of the 24th Annual Conference on Learning Theory.2011:359-376.
[27]AUER P,CESA-BIANCHI N,FREUND Y,et al.The Non-Stochastic Multiarmed Bandit Problem [J].SIAM Journal on Computing,2002,32(1):48-77.
[28]FREUND Y,SCHAPIRE R E.A Decision-Theoretic Generalization of On-Line Learning and An Application to Boosting [J].Journal of Computer and System Sciences,1997,55(1):119-139.
[29]BARD N D C.Online Agent Modelling in Human-Scale Problems [D].Edmonton:University of Alberta,2016.
[30]CESA-BIANCHI N,LUGOSI G.Prediction,Learning,andGames [M].Cambridge:Cambridge university press,2006.
[31]ARORA R,DEKEL O,TEWARI A.Online Bandit LearningAgainst an Adaptive Adversary:From Regret to Policy Regret.[EB/OL].(2012-06-27) [2022-12-01].https://arxiv.org/abs/1206.6400.
[32]LITTLESTONE N,WARMUTH M K.The Weighted Majority Algorithm [J].Information and Computation,1994,108(2):212-261.
[33]WARMUTH M K,JAGOTA A K.Continuous and Discrete-Time Nonlinear Gradient Descent:Relative Loss Bounds and Convergence [C]//Electronic Proceedings of the 5th International Symposium on Artificial Intelligence and Mathematics.1997.
[34]GORDON G J.Regret Bounds for Prediction Problems [C]//Proceedings of the Twelfth Annual Conference on Computa-tional Learning Theory.1999:29-40.
[35]MORRILL D.Hindsight Rational Learning for Sequential Decision-Making:Foundations and Experimental Applications [D].Alberta:University of Alberta,2022.
[36]NEU G.Explore No More:Improved High-Probability Regret Bounds for Non-Stochastic Bandits [C]//Proceedings of the 28th International Conference on Neural Information Processing Systems-Volume 2.2015:3168-3176.
[37]ABERNETHY J,RAKHLIN A.Beating the Adaptive Bandit with High Probability [C]//Proceedings of the Information Theory and Applications Workshop.2009:280-289.
[38]ABERNETHY J,HAZAN E E,RAKHLIN A.Competing inthe Dark:An Efficient Algorithm for Bandit Linear Optimization [C]//Proceedings of the 21st Annual Conference on Learning Theory(COLT 2008).2008:263-273.
[39]NEU G,BARTÓK G.An Efficient Algorithm for Learning with Semi-Bandit Feedback [C]//Proceedings of the International Conference on Algorithmic Learning Theory.2013:234-248.
[40]DANI V,KAKADE S M,HAYES T.The Price of Bandit Information for Online Optimization [C]//Proceedings of the 20th International Conference on Neural Information Processing Systems.2007:345-352.
[41]ADAM L,HORCIK R,KASL T,et al.Double Oracle Algorithm for Computing Equilibria in Continuous Games [C]//Procee-dings of the AAAI Conference on Artificial Intelligence.2021:5070-5077.
[42]GANZFRIED S.Algorithm for Computing Approximate NashEquilibrium in Continuous Games with Application to Continuous Blotto [J].Games,2021,12(2):47.
[43]BEHNEZHAD S,BLUM A,DERAKHSHAN M,et al.FromBattlefields to Elections:Winning Strategies of Blotto and Auditing Games [C]//Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms.2018:2291-2310.
[44]BEHNEZHAD S,DEHGHANI S,DERAKHSHAN M,et al.Faster and Simpler Algorithm for Optimal Strategies of Blotto Game [C]//Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence.2017:369-375.
[45]KOVENOCK D,ROBERSON B.Generalizations of the General Lotto and Colonel Blotto Games [J].Economic Theory,2021,71(3):997-1032.
[46]VU D Q,LOISEAU P,SILVA A.Approximate Equilibria inNon-constant-sum Colonel Blotto and Lottery Blotto Games with Large Numbers of Battlefields [EB/OL].(2019-10-15) [2022-12-01].https://arxiv.org/abs/1910.06559v1.
[47]ROBERSON B.The Colonel Blotto Game [J].Economic Theory,2006,29(1):1-24.
[48]SCHWARTZ G,LOISEAU P,SASTRY S S.The Heteroge-neous Colonel Blotto Game [C]//2014 7th International Confe-rence on Network Games,Control and Optimization(NetGCoop).2014:232-238.
[49]VU D Q,LOISEAU P,SILVA A.Approximate Equilibria inGeneralized Colonel Blotto and Generalized Lottery Blotto Games [EB/OL].(2019-10-15) [2022-12-01].https://arxiv.org/abs/1910.06559v2.
[50]LI X,ZHENG J.Pure strategy Nash equilibrium in 2-Contestant Generalized Lottery Colonel Blotto Games [J].Journal of Mathematical Economics,2022,103:102771.
[51]TULLOCK G.Efficient rent-seeking revisited[M]//The Political Economy of Rent-seeking.Boston,MA:Springer US,1988:91-94.
[52]VU D Q,LOISEAU P.Colonel Blotto Games with Favoritism:Competitions with Pre-Allocations and Asymmetric Effectiveness [C]//Proceedings of the 22nd ACM Conference on Economics and Computation.2021:862-863.
[53]ASPECT L,EWERHART C.Colonel Blotto Games with AHead Start [R].Department of Economics-University of Zu-rich,2022.
[54]GUPTA A,SCHWARTZ G,LANGBORT C,et al.A Three-Stage Colonel Blotto Game with Applications to Cyber Physical Security [C]//Proceedings of the American Control Confe-rence.2014:3820-3825.
[55]PAARPORN K,CHANDAN R,KOVENOCK D,et al.Strategically Revealing Intentions in General Lotto Games [EB/OL].(2021-10-23) [2022-12-01].https://arxiv.org/abs/2110.12099.
[56]VU D Q,LOISEAU P,SILVA A,et al.Path Planning Problems with Side Observations－When Colonels Play Hide And-Seek [C]//Proceedings of the AAAI Conference on Artificial Intelligence.2020:2252-2259.
[57]TAKIMOTO E,WARMUTH M K.Path Kernels and Multipli-cative Updates [J].The Journal of Machine Learning Research,2003,4:773-818.
[58]CZARNECKI W M,GIDEL G,TRACEY B,et al.Real World Games Look Like Spinning Tops [C]//In Proceedings of the 34th International Conference on Neural Information Processing Systems.2020:17443-17454.
[59]OMIDSHAFIEI S,TUYLS K,CZARNECKI W M,et al.Navigating the Landscape of Multiplayer Games [J].Nature Communications.2020,11(1):1-17.
[60]HORTALA-VALLVE R,LLORENTE-SAGUER A.PureStrategy Nash Equilibria in Non-Zero Sum Colonel Blotto Games [J].International Journal of Game Theory,2012,41(2):331-343.
[61]AHMADINEJAD A,DEHGHANI S,HAJIAGHAYI M,et al.From Duels to Battlefields:Computing Equilibria of Blotto and Other Games [J].Mathematics of Operations Research,2019,44(4):1304-1325.
[62]BAYE M R,KOVENOCK D,DE VRIES C G.The Solution to The Tullock Rent-Seeking Game When R> 2:Mixed-Strategy Equilibria and Mean Dissipation Rates [J].Public Choice,1994,81(3):363-380.
[63]HILLMAN A L,RILEY J G.Politically Contestable Rents and Transfers [J].Economics & Politics,1989,1(1):17-39.
[64]MCMAHAN H B,GORDON G J,BLUM A.Planning in The Presence of Cost Functions Controlled by An Adversary [C]//Proceedings of the 20th International Conference on Machine Learning(ICML-03).2003:536-543.
[65]LANCTOT M,ZAMBALDI V,GRUSLYS A,et al.A Unified Game-Theoretic Approach to Multiagent Reinforcement Lear-ning [C]//Proceedings of the 31th International Conference in Neural Information Processing Systems.2017:4193-4206.
[66]ZOU M,CHEN J,LUO J,et al.Equilibrium Approximating andOnline Learning for Anti-Jamming Game of Satellite Communication Power Allocation [J].Electronics,2022,11(21):3526.
[67]GEMP I,SAVANI R,LANCTOT M,et al.Sample-based Approximation of Nash in Large Many-Player Games via Gradient Descent[C]//Proceedings of the 21st International Conference on Autonomous Agents and Multiagent Systems.2022:507-515.
[68]ANTHONY T,ECCLES T,TACCHETTI A,et al.Learning To Play No-Press Diplomacy with Best Response Policy Iteration[C]//Proceedings of the 34th International Conference on Neural Information Processing Systems.2020:17987-18003.
[69]JACOB A P,WU D J,FARINA G,et al.Modeling StrongandHuman-Like Gameplay With KL-Regularized Search[C]//International Conference on Machine Learning.PMLR,2022:9695-9728.
[70]STRANG A,SEWELL D,KIM A,et al.Principal Trade-offAnalysis [EB/OL].(2022-06-09) [2022-12-01].https://arxiv.org/abs/2206.07520.
[71]BERTRAND Q,CZARNECKI W M,GIDEL G.On the Limitations of Elo:Real-World Games,are Transitive,not Additive [EB/OL].(2022-06-21) [2022-12-01].https://arxiv.org/abs/2206.12301.
[72]CHEN W,WANG Y,YUAN Y,et al.Combinatorial Multi-Armed Bandit and Its Extension to Probabilistically Triggered Arms [J].The Journal of Machine Learning Research,2016,17(1):1746-1778.
[73]KOOLEN W M,WARMUTH M K,KIVINEN J,et al.Hedging Structured Concepts [C]//Proceedings of the COLT.2010:93-105.
[74]ALON N,CESA-BIANCHI N,DEKEL O,et al.Online Learning with Feedback Graphs:Beyond Bandits [C]//Proceedings of the Conference on Learning Theory.2015:23-35.
[75]CESA-BIANCHI N,LUGOSI G.Combinatorial Bandits [J].Journal of Computer and System Sciences,2012,78(5):1404-1422.
[76]VU D Q,LOISEAU P,SILVA A.Combinatorial Bandits for Sequential Learning in Colonel Blotto Games [C]//Proceedings of the IEEE 58th Conference on Decision and Control(CDC).2019:867-872.
[77]BADANIDIYURU A,KLEINBERG R,SLIVKINS A.Banditswith Knapsacks [J].Journal of the ACM(JACM),2018,65(3):1-55.
[78]IMMORLICA N,SANKARARAMAN K A,SCHAPIRE R,et al.Adversarial Bandits with Knapsacks [C]//Proceedings of the IEEE 60th Annual Symposium on Foundations of Computer Science(FOCS).2019:202-219.
[79]AGRAWAL S,DEVANUR N.Linear Contextual Bandits with Knapsacks [C]//Proceedings of the 30th International Confe-rence on Neural Information Processing Systems.2016:3458-3467.
[80]LIU S,JIANG J,LI X.Non-stationary Bandits with Knapsacks [EB/OL].(2022-05-25) [2022-12-01].https://arxiv.org/abs/2205.12427.
[81]CASTIGLIONI M,CELLI A,KROER C.Online Learning with Knapsacks:The Best of Both Worlds [EB/OL].(2022-02-28).[2022-12-01] https://arxiv.org/abs/2202.13710.
[82]GAITONDE J,LI Y,LIGHT B,et al.Budget Pacing in Repeated Auctions:Regret and Efficiency without Convergence [EB/OL].(2022-05-18) [2022-12-01].https://arxiv.org/abs/2205.08674.
[83]ASHWINKUMAR B,ROBERT K,ALEKSANDRS S.Bandits with Knapsacks [C]//Proceedings of the 54th IEEE Symposium on Foundations of Computer Science.ACM,2013.
[84]AGRAWAL S,DEVANUR N R.Bandits with Concave Rewards and Convex Knapsacks [C]//Proceedings of the Fifteenth ACM Conference on Economics and Computation.2014:989-1006.
[85]AGRAWAL S,DEVANUR N R,LI L.An Efficient Algorithm for Contextual Bandits with Knapsacks,and An Extension to Concave Objectives [C]//Proceedings of the Conference on Learning Theory.2016:4-18.
[86]BADANIDIYURU A,LANGFORD J,SLIVKINS A.Resourceful Contextual Bandits [C]//Proceedings of the Conference on Learning Theory.2014:1109-1134.
[87]AGARWAL A,HSU D,KALE S,et al.Taming the Monster:A Fast and Simple Algorithm for Contextual Bandits [C]//Proceedings of the International Conference on Machine Learning.2014:1638-1646.
[88]LI X,SUN C,YE Y.The Symmetry between Arms and Knap-sacks:A Primal-Dual Approach for Bandits with Knapsacks [C]//Proceedings of the International Conference on Machine Learning.2021:6483-6492.
[89]LEON V,ETESAMI S R.Bandit Learning for Dynamic Colonel Blotto Game with A Budget Constraint [C]//Proceedings of the 60th IEEE Conference on Decision and Control(CDC).2021:3818-3823.
[90]SANKARARAMAN K A,SLIVKINS A.Combinatorial Semi-Bandits with Knapsacks [C]//Proceedings of the International Conference on Artificial Intelligence and Statistics.2018:1760-1770.
[91]WONG R T.Combinatorial Optimization:Algorithms and Complexity [J].SIAM Review,1983,25(3):424.
[92]CLEMPNER J B.Reveling Misleading Information for Defenders and Attackers in Repeated Stackelberg Security Games [J].Engineering Applications of Artificial Intelligence,2022,110:104703.
[93]CHANDAN R,PAARPORN K,MARDEN J R.When Showing Your Hand Pays Off:Announcing Strategic Intentions in Colonel Blotto Games [C]//Proceedings of the American Control Conference(ACC).2020:4632-4637.
[94]SEDDIGHIN S.Campaigning via LP’s:Solving Blotto and Beyond [D].Baltimore:University of Maryland,2019.
[95]FERGUSON B L,SHISHIKA D,MARDEN J R.Ensuring the Defense of Paths and Perimeters in Dynamic Defender-Attacker Blotto Games(dDAB) on Graphs [C]//Proceedings of the 58th Annual Allerton Conference on Communication,Control,and Computing(Allerton).2022:1-7.
[96]CHEN A K,FERGUSON B L,SHISHIKA D,et al.Path Defense in Dynamic Defender-Attacker Blotto Games(dDAB) with Limited Information [EB/OL].(2022-04-08) [2022-12-01].https://arxiv.org/abs/2204.04176.
[97]PAARPORN K,CHANDAN R,ALIZADEH M,et al.A General Lotto Game with Asymmetric Budget Uncertainty [EB/OL].(2021-06-23) [2022-12-01].https://arxiv.org/abs/2106.12133.
[98]SHAH V,MARDEN J R.Battlefield transfers in coalitionalBlotto games [EB/OL].(2023-04-04) [2023-06-30].https://arxiv.org/abs/2304.02068.
[99]EWERHART C,KOVENOCK D.A Class of N-Player Colonel Blotto Games with Multidimensional Private Information[J].Operations Research Letters,2021,49(3):418-425.
[100]ANBARCI N,CINGIZ K,ISMAIL M S.Proportional ResourceAllocation in Dynamic N-Player Blotto Games[J].Mathematical Social Sciences,2023,125:94-100.
[101]GUAN S,WANG J,JIANG C,et al.Colonel Blotto Game Aided Attack-Defense Analysis in Real-World Networks[C]//2018 IEEE Global Communications Conference(GLOBECOM).IEEE,2018:1-6.
[102]BOIX-ADSERÀ E,EDELMAN B L,JAYANTI S.The Multi-player Colonel Blotto Game[C]//Proceedings of the 21st ACM Conference on Economics and Computation.2020:47-48.
[103]DONAHUE K,KLEINBERG J.Private Blotto:Viewpoint Competition with Polarized Agents [EB/OL].(2023-02-27) [2023-06-30].https://arxiv.org/abs/2302.14123.
[104]PERCHET V,RIGOLLET P,LE GOUIC T.An Algorithmic Solution to The Blotto Game Using Multi-Marginal Couplings [C]//Proceedings of the 23rd ACM Conference on Economics and Computation.2022:208-209.
[105]BEAGLEHOLE D,HOPKINS M,KANE D,et al.SamplingEquilibria:Fast No-Regret Learning in Structured Games [EB/OL].(2022-01-26) [2022-12-01].https://arxiv.org/abs/2201.10758.
[106]NOEL J C G.Reinforcement Learning Agents in Colonel Blotto [EB/OL].(2022-04-04) [2022-12-01].https://arxiv.org/abs/2204.02785.
[107]THOMAS C.N-Dimensional Blotto Game with Heterogeneous Battlefield Values [J].Economic Theory,2018,65(3):509-544.
[108]MASUCCI A M,SILVA A.DefensiveResource Allocation in Social Networks[C]//2015 54th IEEE Conference on Decision and Control(CDC).IEEE,2015:2927-2932.
[109]ZOU M,CHEN J,LUO J,et al.Equilibrium Approximating and Online Learning for Anti-Jamming Game of Satellite Communication Power Allocation[J].Electronics,2022,11(21):3526.
[110]ZHANG L,WANG Y,HAN Z.Safeguarding UAV-EnabledWireless Power Transfer Against Aerial Eavesdropper:A Colonel Blotto Game[J].IEEE Wireless Communications Letters,2021,11:503-507.
[111]WEI P,WANG S D,LU R M,et al.Multi-Channel Power Distribution for Anti-Jamming Based on Asymmetric Colonel Blotto Game [J].Journal of National University of Defense Techno-logy,2023,45:35-48.
[112]HAJIMIRSADEGHI M,SRIDHARAN G,SAAD W,et al.In-ter-Network Dynamic Spectrum Allocation Via a Colonel Blotto Game [C]//Proceedings of the Annual Conference on Information Science and Systems(CISS).2016:252-257.
[113]MIN M,XIAO L,XIE C,et al.Defense Against Advanced Persistent Threats:A Colonel Blotto Game Approach [C]//Proceedings of the IEEE International Conference on Communications(ICC).2017:1-6.
[114]GUAN S,WANG J,YAO H,et al.Colonel blotto games in network systems:Models,strategies,and applications[J].IEEE Transactions on Network Science and Engineering,2019,7(2):637-649.
[115]FERDOWSI A,SAAD W,MANDAYAM N B.Colonel BlottoGame for Sensor Protection in Interdependent Critical Infrastructure[J].IEEE Internet of Things Journal,2020,8(4):2857-2874.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

Comments

Recommended 0

No Suggested Reading articles found!

Research Progress on Colonel Blotto Game Models and Solving Methods

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 0

[1]	CHEN Yipeng, YANG Zhe, GU Fei, ZHAO Lei. Resource Allocation Strategy Based on Game Theory in Mobile Edge Computing [J]. Computer Science, 2023, 50(2): 32-41.
[2]	LI Xiaohuan, CHEN Bitao, KANG Jiawen, YE Jin. Coalition Game-assisted Joint Resource Optimization for Digital Twin-assisted Edge Intelligence [J]. Computer Science, 2023, 50(2): 42-49.
[3]	YU Bin, LI Xue-hua, PAN Chun-yu, LI Na. Edge-Cloud Collaborative Resource Allocation Algorithm Based on Deep Reinforcement Learning [J]. Computer Science, 2022, 49(7): 248-253.
[4]	TANG Feng, FENG Xiang, YU Hui-qun. Multi-task Cooperative Optimization Algorithm Based on Adaptive Knowledge Transfer andResource Allocation [J]. Computer Science, 2022, 49(7): 254-262.
[5]	LI Meng-fei, MAO Ying-chi, TU Zi-jian, WANG Xuan, XU Shu-fang. Server-reliability Task Offloading Strategy Based on Deep Deterministic Policy Gradient [J]. Computer Science, 2022, 49(7): 271-279.
[6]	ZHOU Tian-qing, YUE Ya-li. Multi-Task and Multi-Step Computation Offloading in Ultra-dense IoT Networks [J]. Computer Science, 2022, 49(6): 12-18.
[7]	QIU Xu, BIAN Hao-bu, WU Ming-xiao, ZHU Xiao-rong. Study on Task Offloading Algorithm for Internet of Vehicles on Highway Based on 5G MillimeterWave Communication [J]. Computer Science, 2022, 49(6): 25-31.
[8]	XU Hao, CAO Gui-jun, YAN Lu, LI Ke, WANG Zhen-hong. Wireless Resource Allocation Algorithm with High Reliability and Low Delay for Railway Container [J]. Computer Science, 2022, 49(6): 39-43.
[9]	SHEN Jia-fang, QIAN Li-ping, YANG Chao. Non-orthogonal Multiple Access and Multi-dimension Resource Optimization in EH Relay NB-IoT Networks [J]. Computer Science, 2022, 49(5): 279-286.
[10]	PAN Yan-na, FENG Xiang, YU Hui-qun. Competitive-Cooperative Coevolution for Large Scale Optimization with Computation Resource Allocation Pool [J]. Computer Science, 2022, 49(2): 182-190.
[11]	WU Yun-han, BAI Guang-wei, SHEN Hang. Multi-dimensional Resource Dynamic Allocation Algorithm for Internet of Vehicles Based on Federated Learning [J]. Computer Science, 2022, 49(12): 59-65.
[12]	YUAN Xin-wang, XIE Zhi-dong, TAN Xin. Survey of Resource Management Optimization of UAV Edge Computing [J]. Computer Science, 2022, 49(11): 234-241.
[13]	WANG Ying-kai, WANG Qing-shan. Reinforcement Learning Based Energy Allocation Strategy for Multi-access Wireless Communications with Energy Harvesting [J]. Computer Science, 2021, 48(7): 333-339.
[14]	SONG Hai-ning, JIAO Jian, LIU Yong. Research on Mobile Edge Computing in Expressway [J]. Computer Science, 2021, 48(6A): 383-386.
[15]	WANG Cong, WEI Cheng-qiang, LI Ning, MA Wen-feng, TIAN Hui. Dynamic Allocation Mechanism of Preamble Resources Under H2H and M2M Coexistence Scenarios [J]. Computer Science, 2021, 48(5): 283-288.