Abstract
Much attention has been paid on exploring the solutions for cooperative dilemma in multi-agent systems. Thereinto, the evolutionary game theory which describes cooperative dilemma is seen as an effective approach. Notably, many of previous works are based on the ideal hypothesis that individuals can feasibly obtain their neighbours’ payoffs to update strategies. Considering the difficulty of getting the exact information about payoffs, we propose the switching probabilities between strategies which do not require the payoffs. Here the evolutionary dynamics driven by the switching probabilities in a three-strategy game model is established. Results show that the steady state of the gaming system is closely related with the switching probability matrix. These findings give a novel account about the decision making process in the gaming systems, when a strategy updating rule weakening the ideal assumption about payoffs is established.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Colman AM. Game theory and its applications in the social and biological sciences. Psychology Press;1998.
Axelrod R. The evolution of cooperation. Basic Books;1984.
van den Berg P, Molleman L, Weissing FJ. Focus on the success of others leads to selfish behavior. Proc Natl Acad Sci. 2015;112(9):2912–7.
Lamba S. Social learning in cooperative dilemmasr. Proc R Soc Lond B Biol Sci. 2014;281(1787):20140417.
Nowak MA. Five rules for the evolution of cooperation. Science. 2006;314:1560–3.
Stewart AJ, Plotkin JB. Small groups and long memories promote cooperation. Sci Rep. 2016;6(s 1–3):26889.
Stivala A, Kashima Y, Kirley M. Culture and cooperation in a spatial public goods game. Phys Rev E. 2016;94(3):032303.
Scott B. Coordination vs. voluntarism and enforcement in sustaining international environmental cooperation. Proc Nat Acad Sci. 2016;113(51):14515–22.
Smith JM. Evolution and the theory of games. Cambridge University Press;1982.
Cimini G, Sánchez A. Learning dynamics explains human behaviour in prisoners dilemma on networks. J R Soc Interface. 2014;11(94):20131186.
Poncela J, Gómez-Gardeñes J. Cooperation in scale-free networks with limited associative capacities. Phys Rev E. 2011;83(5).
Sasaki T, Okada I. Cheating is evolutionarily assimilated with cooperation in the continuous snowdrift game. BioSystems. 2015;131:51–9.
Abbass H, Greenwood G, Petraki E. The n-player trust game and its replicator dynamics. IEEE Trans Evol Comput. 2016;20(3):470–4.
Bomze IM. Lotka-volterra equation and replicator dynamics: new issues in classification. Biol Cybern. 1995;72:447–53.
Taylor P, Jonker L. Evolutionarily stable strategies and game dynamics. Math Biosci. 1978;40:145–56.
Nowak MA, Sigmund K. Evolution of cooperation by multilevel selection. Proc Natl Acad Sci. 2006;103(29):10952–5.
Vainstein MH, Arenzon JJ. Spatial social dilemmas: dilution, mobility and grouping effects with imitation dynamics. Physica A. 2014;394:145–57.
Fosco C, Mengel F. Cooperation through imitation and exclusion in networks. J Econ Dyn Control. 2011;35:641–58.
Galla T. Imitation, internal absorption and the reversal of local drift in stochastic evolutionary games. J Theoret Biol. 2011;269:46–56.
Sánchez A, Vilone D, Ramasco J, San Miguel M. Social imitation versus strategic choice, or consensus versus cooperation, in the networked prisoners dilemma. Phys Rev E. 2014;90(2):022810.
Traulsen A, Claussen JC, Hauert C, San M. Coevolutionary dynamics: from finite to infinite populations. Phys Rev Lett. 2005;95:238701.
Blume LE. The statistical mechanics of best-response strategy revision. Games Econ Behav. 1995;5(387):111–45.
Hauert C, Szabo G. Game theory and physics. Am J Phys. 2005;73(5):405–14.
Helbing D. A stochastic behavioral model and a microscopic foundation of evolutionary game theory. Theory Decis. 1996;40:149–79.
Blume LE. How noise matters. Games Econ Behav. 2003;44(2):251–71.
Zhang J, Zhang C, Chu T. The evolution of cooperation in spatial groups. Chaos Solitons Fractals. 2011;44:131–6.
Zhang J, Zhang C, Cao M, Weissing FJ. Crucial role of strategy updating for coexistence of strategies in interaction networks. Phys Rev E. 2015;91(4):042101.
Zhang J, Chen Z. Contact-based model for strategy updating and evolution of cooperation. Physica D. 2016;323–3242:27–34.
Xu Z, Zhang J, Zhang C, Chen Z. Fixation of strategies driven by switching probabilities in evolutionary games. EPL. 2016;116(5):58002.
Acknowledgements
We acknowledge the financial support from the National Natural Science Foundation of China (Grant Nos. 61603199 and 61603201 and 61573199).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Xu, Z., Zhang, J., Li, Q., Chen, Z. (2018). Decision Making in Multi-agent Systems Based on the Evolutionary Game with Switching Probabilities. In: Jia, Y., Du, J., Zhang, W. (eds) Proceedings of 2017 Chinese Intelligent Systems Conference. CISC 2017. Lecture Notes in Electrical Engineering, vol 459. Springer, Singapore. https://doi.org/10.1007/978-981-10-6496-8_12
Download citation
DOI: https://doi.org/10.1007/978-981-10-6496-8_12
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-6495-1
Online ISBN: 978-981-10-6496-8
eBook Packages: EngineeringEngineering (R0)