4 Simulation
4.2 APBSG on Scale-Free Network
Going beyond small-world, we also investigate the APBSG on scale-free network.
Figure4shows the simulation results on the Barab´asi-Albert network.
Result in Fig.4 shows that similar to the results in the small-world network, the frequency of cooperation linearly decreases when payoff ratio r increases in scale-free network. However, there’re still about 80 % nodes choose cooperation strategy while in small-world it’s about 70 % when r = 1, and the sensitivity θ(r) of the frequency of cooperation is 0.15, which is lower than that in small- world network. This indicates that scale-free network is more likely to promote emergence of cooperation than small-world network because of the wider range of degree distribution in scale-free network.
Figure5 shows how the frequency of cooperation changes with the different degrees in scale-free network when r = 0.2. It can be easily seen that only the nodes with larger degrees tend to be “pure cooperators”, while most of the other nodes tend to be “strategy swingers”, which is very different from that in small-world. Thus we can increase the heterogeneity of nodes for P2P network to improve the frequency of cooperation and guarantee the stability of the network.
170 180 190 200 210 220 230 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Degree of Nodes
strategy distribution per degree
Cooperation Defect
Fig. 3.Distributions of strategies in small-world network. Cooperators and defectors are denoted by gray bars and black bars respectively. Each bar adds up to a total fraction of 1 per degree, the gray and black fractions being directly proportional to relative percentage of respective strategy for each degree. Those nodes which have middle degrees will choose the cooperation strategy in one round and maybe defect for next round. In contrast, those having smaller or larger degrees tend to adhere to the cooperative behavior no matter what strategy their neighbors take.
0 0.2 0.4 0.6 0.8 1
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Cost to payoff ratio r
Frequency of Cooperators
APBSG MBSG
k=−0.15
k=−0.60
Fig. 4. fC as a function of r in scale-free network whose size is 2500. fC for each simulation is obtained by averaging from time stept= 1000 to 5000 where the system has reached a steady state.
50 100 150 200 250 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Degree of Nodes
strategy distribution per degree
Cooperation Defect
Fig. 5. Distributions of strategies in scale-free network. Cooperators and defectors are denoted by gray bars and black bars respectively. Each bar adds up to a total fraction of 1 per degree, the gray and black fractions being directly proportional to relative percentage of respective strategy for each degree. Those nodes which have smaller degrees will choose the cooperation strategy in one round and maybe defect for next round. In contrast, those having larger degrees tend to adhere to the cooperative behavior no matter what strategy their neighbors take.
5 Conclusion
In this paper, we have investigated the cooperative behavior in the P2P file sharing system and found that it’s essentially a snowdrift game. A novel incen- tive mechanism called Accumulated-Payoff Based Snowdrift Game is adapted to guarantee a high proportion of cooperation and maintain a continuing stability of the P2P network. The results show that APBSG can reduce the sensitivity of cooperation to the selfishness of nodes, which greatly promotes the coopera- tive behavior in P2P network. Meanwhile, the results also give a relationship of frequency of cooperation and the degrees of nodes. Nodes with larger or smaller degrees promote the emergence of cooperative behavior in small-world network, while in scale-free networks, the larger degree nodes tend to be pure cooperators.
In current work, the topology of network is static, and this assumption is true for some cases. In future work, we will investigate the incentive mechanism in the situation when nodes can withdraw from or add dynamically in to the P2P network.
Acknowledgment. This work was supported by the NSFC China under projects 61371079, 61471025, 61271267 and 91338203, and the Open Research Fund of National Mobile Communications Research Laboratory, Southeast University (No. 2016D07).
References
1. Lua, E.K., Croowcroft, J., Pias, M.: A survey and comparition of peer-to-peer overlay network schemes. J. IEEE Commun. Surv. Tutorial7(2), 72–93 (2005) 2. Adar, E., Huberman, B.: Free riding on gnutella. First Monday 5(10), 305–314
(2000)
3. Hughes, D., Goulson, G., Walkerdine, J.: Free riding gnurella revisited: the bell tolls? IEEE Distrib. Syst. Online6(6), 276–277 (2005)
4. Saroiu, S., Gummadi, P., Gribble, S.D.: A measurement study of peer-to-peer file sharing systems. In: Proceeding of the Multimedia Computing and Networking 2002 (MMCN 2002), pp. 156–170 (2002)
5. Sugden, R.: The economics of rights, co-operation and welfare (1986) 6. Smith, M.: Evolution and the theory of games. Am. Sci.64(1), 41–45 (1976) 7. Smith, M., P. G. R.: The logic of animal conflict. Nature 246(5427), 15–18 (1973) 8. Jiang, C., Chen, Y., Liu, K.J.R.: Data-driven route selection and throughput analy-
sis in cognitive vehicular networks. IEEE J. Sel. Areas Commun.32(11), 2149–2162 (2014)
9. Jiang, C.: Graphical evolutionary game for information diffusion over social net- works. IEEE J. Sel. Topics Signal Process.8(4), 524–536 (2014)
10. Jiang, C.: Evolutionary dynamics of information diffusion over social networks.
IEEE Trans. Signal Process.62(17), 4573–4586 (2014)
11. Jiang, C., Chen, Y., Gao, Y., Liu, K.J.R.: Joint spectrum sensing and access evolu- tionary game in cognitive radio networks. IEEE Trans. Wireless Commun.12(5), 2470–2483 (2013)
12. Jiang, C., Chen, Y., Liu, K.J.R.: Distributed adaptive networks: a graphical evo- lutionary game theoretic view. IEEE Trans. Signal Process. 61(22), 5675–5688 (2013)
13. Jiang, C., Chen, Y., Yang, Y., Wang, C., Liu, K.J.R.: Dynamic chinese restaurant game: theory and application to cognitive radio networks. IEEE Trans. Wireless Commun.13(4), 1960–1973 (2014)
14. Zhang, N.B.X.C.X.W.H., Jiang, C., Quek, T.Q.: Resource allocation for cogni- tive small cell networks: A cooperative bargaining game theoretic approach. IEEE Trans. Wireless Commun.14(6), 3481–3493 (2015)
15. Zhang, H.: Resource allocation with interference mitigation in ofdma femtocells for co-channel deployment. EURASIP J. Wireless Commun. Networking 89, (2012) 16. Jiang, C., Chen, Y., Liu, K.J.R.: Multi-channel sensing and access game: Bayesian
social learning with negative network externality. IEEE Trans. Wireless Commun.
13(4), 2176–2188 (2014)
17. Albert, R., Barab´asi, A.-L.: Statistical mechanics of complex networks. Rev. Mod.
Phys.74, 47–97 (2002)
18. Boudec, J.Y.L., Vojnovic, M.: Perfect simulation and stationarity of a class of mobility models. In: Proceedings of IEEE INFOCOM 2005, pp. 72–79 (2005) 19. Watts, D.J., Strogatz, S.H.: Collective dynamics of ’small-world’ networks. Nature
393, 440–442 (1998)
20. Barab´asi, A.L., Albert, R.: Diameter of the world-wide web. Nature401, 130–131 (1999)
21. Wang, W.X., Ren, J., Chen, G., Wang, B.H.: Memory-based snowdrift game on networks. Phys. Rev. E74, 56–113 (2006)