Abstract
In this paper, a general resource distribution game with a hierarchical structure on the bipartite graph is proposed. In this system, the game is divided into two interacting levels, the agent level and the group level, with negotiations taking place on both levels. Each agent can belong to multiple groups, resulting in a system topology with a bipartite structure. On the agent level, decisions are based on the greedy principle, with the game being a state-based potential game. In contrast, some participants on the group level behave more “smartly” and are more likely to adopt a sophisticated strategy maximizing their personal interest. Strategies on both levels are based on distributed protocols, and the social welfare increases as the system approaches a Nash-equilibrium point. The designed protocols are theoretically analyzed from stability and efficiency. Furthermore, a reinforcement learning algorithm is introduced in the group level, where the smarter players are allowed to refine their strategies in the multi-step decision-making process by learning from historic game outcomes. In theory and according to simulations, agents with the learning behavior improve not only their personal interest but also the efficiency of the systemic resource distribution.
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Quijano N, Ocampo-Martinez C, Barreiro-Gomez J, et al. The role of population games and evolutionary dynamics in distributed control systems: the advantages of evolutionary game theory. IEEE Control Syst, 2017, 37: 70–97
Nowak M A, Tarnita C E, Antal T. Evolutionary dynamics in structured populations. Phil Trans R Soc B, 2010, 365: 19–30
Fu F, Wang L, Nowak M A, et al. Evolutionary dynamics on graphs: efficient method for weak selection. Phys Rev E, 2009, 79: 046707
Taylor C, Fudenberg D, Sasaki A, et al. Evolutionary game dynamics in finite populations. Bull Math Biol, 2004, 66: 1621–1644
Ohtsuki H, Nowak M A. Evolutionary games on cycles. Proc R Soc B, 2006, 273: 2249–2256
Nowak M A. Five rules for the evolution of cooperation. Science, 2006, 314: 1560–1563
Ohtsuki H, Nowak M A, Pacheco J M. Breaking the symmetry between interaction and replacement in evolutionary dynamics on graphs. Phys Rev Lett, 2007, 98: 108106
Tarnita C E, Ohtsuki H, Antal T, et al. Strategy selection in structured populations. J Theory Biol, 2009, 259: 570–581
Xia C Y, Li X P, Wang Z, et al. Doubly effects of information sharing on interdependent network reciprocity. New J Phys, 2018, 20: 075005
Tang C B, Li X, Wang Z, et al. Cooperation and distributed optimization for the unreliable wireless game with indirect reciprocity. Sci China Inf Sci, 2017, 60: 110205
Xia C Y, Ding S, Wang C J, et al. Risk analysis and enhancement of cooperation yielded by the individual reputation in the spatial public goods game. IEEE Syst J, 2017, 11: 1516–1525
Chen M H, Wang L, Sun S W, et al. Evolution of cooperation in the spatial public goods game with adaptive reputation assortment. Phys Lett A, 2016, 380: 40–47
Fudenberg D, Levine D K. The Theory of Learning in Games. Boston: MIT Press, 1998
Li J Q, Zhang C Y, Sun Q L, et al. Changing intensity of interaction can resolve prisoner’s dilemmas. Europhys Lett, 2016, 113: 58002
Perc M, Gómez-Gardeñes J, Szolnoki A, et al. Evolutionary dynamics of group interactions on structured populations: a review. J R Soc Interface, 2013, 10: 20120997
Gracia-Lázaro C, Gómez-Gardeñes J, Floría L M, et al. Intergroup information exchange drives cooperation in the public goods game. Phys Rev E, 2014, 90: 042808
Gómez-Gardeñes J, Vilone D, Sánchez A. Disentangling social and group heterogeneities: public goods games on complex networks. EPL, 2011, 95: 68003
Gómez-Gardeñes J, Romance M, Criado R, et al. Evolutionary games defined at the network mesoscale: the public goods game. Chaos, 2011, 21: 016113
Kelly F P, Maulloo A K, Tan D K H. Rate control for communication networks: shadow prices, proportional fairness and stability. J Oper Res Soc, 1998, 49: 237–252
Li J, Ma G Q, Li T, et al. A Stackelberg game approach for demandresponse management of multi-microgrids with overlapping sales areas. Sci China Inf Sci, 2019, 62: 212203
Monderer D, Shapley L S. Potential games. Games Econom Behav, 1996, 16: 124–143
Barreiro-Gomez J, Obando G, Quijano N. Distributed population dynamics: optimization and control applications. IEEE Trans Syst Man Cybern Syst, 2017, 47: 304–314
Barreiro-Gomez J, Quijano N, Ocampo-Martinez C. Constrained distributed optimization: a population dynamics approach. Automatica, 2016, 69: 101–116
Li N, Marden J R. Designing games for distributed optimization. IEEE J Sel Top Signal Process, 2013, 7: 230–242
Li N, Marden J R. Decoupling coupled constraints through utility design. IEEE Trans Autom Control, 2014, 59: 2289–2294
Marden J R. State based potential games. Automatica, 2012, 48: 3075–3088
Maheswaran R, Basar T. Efficient signal proportional allocation (ESPA) mechanisms: decentralized social welfare maximization for divisible resources. IEEE J Sel Areas Commun, 2006, 24: 1000–1009
Yan L, Qu B Y, Zhu Y S, et al. Dynamic economic emission dispatch based on multi-objective pigeon-inspired optimization with double disturbance. Sci China Inf Sci, 2019, 62: 070210
Tang C B, Li A, Li X. Asymmetric game: a silver bullet to weighted vertex cover of networks. IEEE Trans Cybern, 2018, 48: 2994–3005
Li X X, Peng Z H, Liang L, et al. Policy iteration based Q-learning for linear nonzero-sum quadratic differential games. Sci China Inf Sci, 2019, 62: 052204
Watkins C J, Dayan P. Technical note: Q-learning. Mach Learn, 1992, 8: 279–292
Lanctot M, Zambaldi V F, Gruslys A, et al. A unified game-theoretic approach to multiagent reinforcement learning. In: Proceedings of the 31st International Conference on Neural Information Processing, 2017. 4190–4203
Tuyls K, Pérolat J, Lanctot M, et al. Symmetric decomposition of asymmetric games. Sci Rep, 2018, 8: 1015
Zhang K Q, Yang Z R, Liu H, et al. Fully decentralized multi-agent reinforcement learning with networked agents. In: Proceedings of International Conference on Machine Learning, 2018. 5867–5876
Busoniu L, Babuska R, de Schutter B. A comprehensive survey of multiagent reinforcement learning. IEEE Trans Syst Man Cybern C, 2008, 38: 156–172
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This work was supported by Tianjin Natural Science Foundation (Grant Nos. 20JCYBJC01060, 20JCQNJC01450) and National Natural Science Foundation of China (Grant No. 61973175).
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Guo, L., Liu, Z. & Chen, Z. The greedy crowd and smart leaders: a hierarchical strategy selection game with learning protocol. Sci. China Inf. Sci. 64, 132206 (2021). https://doi.org/10.1007/s11432-019-2825-y
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DOI: https://doi.org/10.1007/s11432-019-2825-y