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Iterated n-player games on small-world networks

Published: 12 July 2011 Publication History

Abstract

The evolution of strategies in iterated multi-player social dilemma games is studied on small-world networks. Two different games with varying reward values - the N-player Iterated Prisoner's Dilemma (N-IPD) and the N-player Iterated Snowdrift game (N-ISD) - form the basis of this study. Here, the agents playing the game are mapped to the nodes of different network architectures, ranging from regular lattices to small-world networks and random graphs. In a given game instance, the focal agent participates in an iterative game with N-1 other agents drawn from its local neighbourhood. We use a genetic algorithm with synchronous updating to evolve agent strategies. Extensive Monte Carlo simulation experiments show that for smaller cost-to-benefit ratios, the extent of cooperation in both games decreases as the probability of re-wiring increases. For higher cost-to-benefit ratios, when the re-wiring probability is small we observe an increase in the level of cooperation in the N-IPD population, but not the N-ISD population. This suggests that the small-world network structure with small re-wiring probabilities can both promote and maintain higher levels of cooperation when the game becomes more challenging.

References

[1]
G. Abramson and M. Kuperman. Social games in a social network. Physical Review E, 63:030901, 2001.
[2]
R. Axelrod. The evolution of cooperation. Basic Books: New York, 1984.
[3]
R. Axelrod. The evolution of strategies in the iterated prisoner's dilemma. In L. Davis, editor, Genetic Algorithms and Simulated Annealing, pages 32--41. Morgan Kaufmann, Los Altos, CA, 1987.
[4]
R. Boyd and P. J. Richerson. The evolution of reciprocity in sizable groups. Journal of Theoretical Biology, 132:337--356, 1988.
[5]
C. H. Chan, H. Yin, P. M. Hui, and D. F. Zheng. Evolution of cooperation in well-mixed N-person snowdrift games. Physica A: Statistical Mechanics and its Applications, 387:2919--2925, 2008.
[6]
X. J. Chen and L. Wang. Effects of cost threshold and noise in spatial snowdrift games with fixed multi-person interactions. Europhysics Letters, 90:38003, 2010.
[7]
R. Chiong, S. Dhakal, and L. Jankovic. Effects of neighbourhood structure on evolution of cooperation in N-player iterated prisoner's dilemma. In H. Yin, P. Tino, E. Corchado, W. Byrne, and X. Yao, editors, Intelligent Data Engineering and Automated Learning, volume 4881 of Lecture Notes in Computer Science, pages 950--959. Springer-Verlag, 2007.
[8]
R. Chiong and M. Kirley. Co-evolutionary learning in the N-player iterated prisoner's dilemma with a structured environment. In K. Korb, M. Randall, and T. Hendtlass, editors, Artificial Life: Borrowing from Biology, volume 5865 of Lecture Notes in Artificial Intelligence, pages 32--42. Springer-Verlag, 2009.
[9]
R. Chiong and M. Kirley. Co-evolution of agent strategies in N-player dilemmas. In W. van der Hoek, G. A. Kaminka, Y. Lesp--erance, M. Luck, and S. Sen, editors, Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2010), pages 1591--1592, Toronto, Canada, 2010.
[10]
R. Chiong and M. Kirley. Evolving cooperation in the spatial N-player snowdrift game. In J. Li, editor, AI 2010: Advances in Artificial Intelligence, volume 6464 of Lecture Notes in Artificial Intelligence, pages 263--272. Springer-Verlag, 2010.
[11]
R. Chiong and M. Kirley. Imitation vs evolution: analysing the effects of strategy update mechanisms in N-player social dilemmas. In Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2010), pages 2904--2911. IEEE Press, 2010.
[12]
L. R. Dong. Dynamic evolution with limited learning information on a small-world network. Communications in Theoretical Physics, 54(3):578--582, 2010.
[13]
F. Dubois and L. Giraldeau. The forager's dilemma: Food sharing and food defense as risk-sensitive foraging options. The American Naturalist, 162(6):768--779, 2003.
[14]
F. Fu, L. H. Liu, and L. Wang. Evolutionary prisoner's dilemma on heterogeneous Newman-Watts small-world network. The European Physical Journal B, 56(4):367--372, 2007.
[15]
J. Y. Guan, Z. X. Wu, Z. G. Huang, and Y. H. Wang. Prisoner's dilemma game with nonlinear attractive effect on regular small-world networks. Chinese Physics Letters, 23(10):2874, 2006.
[16]
C. Hauert and G. Szab--o. Game theory and physics. American Journal of Physics, 73(5):405--414, 2005.
[17]
M. Ji, C. Xu, D. F. Zheng, and P. M. Hui. Enhanced cooperation and harmonious population in an evolutionary N-person snowdrift game. Physica A: Statistical Mechanics and its Applications, 389:1071--1076, 2010.
[18]
B. J. Kim, A. Trusina, P. Holme, P. Minnhagen, J. S. Chung, and M. Y. Choi. Dynamic instabilities induced by asymmetric influence: Prisoner's dilemma game in small-world networks. Physical Review E, 66:021907, 2002.
[19]
J. W. Kim. A tag-based evolutionary prisoner's dilemma game on networks with di erent topologies. Journal of Artificial Societies and Social Simulation, 13(3):2, 2010.
[20]
R. Kummerli, C. Colliard, N. Fiechter, B. Petitpierre, F. Russier, and L. Keller. Human cooperation in social dilemmas: Comparing the snowdrift game with the prisoner's dilemma. Proceedings of the Royal Society of London: Biological Sciences, 274:2965--2970, 2007.
[21]
K. H. Lee, C. H. Chan, P. M. Hui, and D. F. Zheng. Cooperation in N-person evolutionary snowdrift game in scale-free Barab--asi-Albert networks. Physica A: Statistical Mechanics and its Applications, 387:5602--5608, 2008.
[22]
X. Li, Y. Wu, Z. Rong, Z. Zhang, and S. Zhou. The prisoner's dilemma in structured scale-free networks. Journal of Physics A: Mathematical and Theoretical, 42:245002, 2009.
[23]
N. Masuda and K. Aihara. Spatial prisoner's dilemma optimally played in small-world networks. Physics Letters A, 313:55--61, 2003.
[24]
M. A. Nowak and R. M. May. Evolutionary games and spatial chaos. Nature, 359:826--829, 1992.
[25]
M. A. Nowak and R. M. May. The spatial dilemmas of evolution. International Journal of Bifurcation and Chaos, 3:35--78, 1993.
[26]
C. O'Riordan, A. Cunningham, and H. Sorensen. Emergence of cooperation in N-player games on small world networks. In S. Bullock, J. Noble, R. Watson, and M. Bedau, editors, Artificial Life XI, pages 436--442. MIT Press, 2008.
[27]
M. Posch, A. Pichler, and K. Sigmund. The efficiency of adapting aspiration levels. Proceedings of the Royal Society of London: Biological Sciences, 266:1427--1435, 1999.
[28]
T. Qiu, T. Hadzibeganovic, G. Chen, L. X. Zhong, and X. R. Wu. Cooperation in the snowdrift game on directed small-world networks under self-questioning and noisy conditions. Computer Physics Communications, 181(12):2057--2062, 2010.
[29]
F. C. Santos and J. M. Pacheco. Scale-free networks provide a unifying framework for the emergence of cooperation. Physical Review Letters, 95:098104, 2005.
[30]
F. C. Santos, J. M. Pacheco, and T. Lenaerts. Cooperation prevails when individuals adjust their social ties. PLoS Computational Biology, 2:1284--1290, 2006.
[31]
F. C. Santos, J. M. Pacheco, and T. Lenaerts. Evolutionary dynamics of social dilemmas in structured heterogeneous populations. Proceedings of the National Academy of Sciences of the USA, 103:3490--3494, 2006.
[32]
F. C. Santos, M. D. Santos, and J. M. Pacheco. Social diversity promotes the emergence of cooperation in public goods games. Nature, 454:213--216, 2008.
[33]
L. H. Shang, X. Li, and X. F. Wang. Cooperative dynamics of snowdrift game on spatial distance-dependent small-world networks. The European Physical Journal B, 54(3):369--373, 2006.
[34]
L. H. Shang, M. J. Zhang, and Y. Q. Yang. Cooperative dynamics in lattice-embedded scale-free networks. Communications in Theoretical Physics, 52:411--415, 2009.
[35]
M. O. Souza, J. M. Pacheco, and F. C. Santos. Evolution of cooperation under N-person snowdrift games. Journal of Theoretical Biology, 260:581--588, 2009.
[36]
G. Szab--o and G. Fath. Evolutionary games on graphs. Physics Reports, 446:97--216, 2007.
[37]
X. Thibert-Plante and L. Parrott. Prisoner's dilemma and clusters on small-world networks. Complexity, 12(6):22--36, 2007.
[38]
M. Tomassini, L. Luthi, and M. Giacobini. Hawks and doves games on small-world networks. Physical Review E, 73:016132, 2006.
[39]
M. Tomochi. Defectors' niches: prisoner's dilemma game on disordered networks. Social Networks, 26(4):309--321, 2004.
[40]
R. L. Trivers. The evolution of reciprocal altruism. The Quarterly Review of Biology, 46(1):35--57, 1971.
[41]
D. Watts and S. H. Stogatz. Collective dynamics of small-world networks. Nature, 393:440--442, 1998.
[42]
Z. X. Wu, X. J. Xu, Y. C. Y, and Y. H. Wang. Spatial prisoner's dilemma game with volunteering in Newman-Watts small-world networks. Physical Review E, 71:037103, 2005.
[43]
X. Yao and P. Darwen. An experimental study of N-person iterated prisoner's dilemma games. Informatica, 18(4):435--450, 1994.
[44]
M. F. Zhang, B. H. Wang, W. X. Wang, C. L. Tang, and R. Yang. Randomness effect on cooperation in memory-based snowdrift game. Chinese Physics Letters, 25(4):1494--1497, 2008.
[45]
D. F. Zheng, H. P. Yin, C. H. Chan, and P. M. Hui. Cooperative behavior in a model of evolutionary snowdrift games with N-person interactions. Europhysics Letters, 80:18002, 2007.
[46]
L. X. Zhong, D. F. Zheng, B. Zheng, C. Xu, and P. M. Hui. Networking effects on cooperation in evolutionary snowdrift game. Europhysics Letters, 76(4):724--730, 2006.

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cover image ACM Conferences
GECCO '11: Proceedings of the 13th annual conference on Genetic and evolutionary computation
July 2011
2140 pages
ISBN:9781450305570
DOI:10.1145/2001576
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 12 July 2011

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Author Tags

  1. iterated n-player games
  2. prisoner's dilemma
  3. small-world networks
  4. snowdrift game

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  • (2015)Using Discrete PSO Algorithm to Evolve Multi-player Games on Spatial Structure EnvironmentAdvances in Swarm and Computational Intelligence10.1007/978-3-319-20472-7_24(219-228)Online publication date: 2-Jun-2015
  • (2014)Graph centrality measures and the robustness of cooperation2014 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC.2014.6900588(1232-1237)Online publication date: Jul-2014
  • (2013)Effect of Spatial Structure on the Evolution of Cooperation in the N-Choice Iterated Prisoner’s DilemmaTransactions on Computational Science XXI10.1007/978-3-642-45318-2_11(253-268)Online publication date: 2013
  • (2012)Effects of Iterated Interactions in Multiplayer Spatial Evolutionary GamesIEEE Transactions on Evolutionary Computation10.1109/TEVC.2011.216768216:4(537-555)Online publication date: 1-Aug-2012
  • (2012)A multimodal problem for competitive coevolutionProceedings of the 25th Australasian joint conference on Advances in Artificial Intelligence10.1007/978-3-642-35101-3_29(338-349)Online publication date: 4-Dec-2012

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