Skip to main content
SpringerLink
Log in

Heterogeneous investment in spatial public goods game with mixed strategy

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Understanding and maximizing the effects of heterogeneous investment, particularly in a socially diverse society, on the evolution of cooperation have been the focus of recent research. In the most existing studies, individuals are limited to make binary decisions (i.e., either cooperate or defect). This is unrealistic in many real-world situations. In this paper, we investigate the effect of a heterogeneous investment on the evolution of cooperation in mixed strategy public goods games, wherein individuals have different probability of cooperation. Specifically, players are able to distribute heterogeneous investments into different groups, and they tend to allocate their investment into the group which achieves a higher return on investment (e.g., payoffs). Simulation results show that the formation of cooperative clusters allows cooperative players to resist the exploitation of defective players; subsequently, the cooperation level of the whole population significantly increases. Moreover, the results also show that cooperative clusters become more robust when the investment redistribution decision relies on more recent information. Our study may offer new insights into how strategy diversity promotes the evolutionary of cooperation in realistic situations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  • Bo X, Wang J, Ruipu D (2014) Relational diversity promotes cooperation in prisoner’s dilemma games. PLoS ONE 9:e114464

    Article  Google Scholar 

  • Brandt H, Hauert C, Sigmund K (2003) Punishment and reputation in spatial public goods games. Biol Sci 270:1099–1104

    Article  Google Scholar 

  • Cao XB, Du WB, Rong ZH (2010) The evolutionary public goods game on scale-free networks with heterogeneous investment. Phys A Stat Mech Appl 389:1273–1280

    Article  Google Scholar 

  • Chen X, Liu Y, Zhou Y (2012) Adaptive and bounded investment returns promote cooperation in spatial public goods games. PLoS ONE 7:e36895

    Article  Google Scholar 

  • Christoph H, Arne T, Hannelore B (2007) Via freedom to coercion: the emergence of costly punishment. Science 316:1905–1907

    Article  MathSciNet  MATH  Google Scholar 

  • Fu Z, Ren K, Shu J, Sun X, Huang F (2015) Enabling personalized search over encrypted outsourced data with efficiency improvement. IEEE Trans Parallel Distrib Syst 27(9):2546–2559

    Article  Google Scholar 

  • Fu Z, Sun X, Liu Q, Zhou L, Shu J (2015) Achieving efficient cloud search services: multi-keyword ranked search over encrypted cloud data supporting parallel computing. IEICE Trans Commun 98(1):190–200

    Article  Google Scholar 

  • Gao J, Li Z, Wu T (2007) Diversity of contribution promotes cooperation in public goods games. Phys A Stat Mech Appl 389:3166–3171

    Article  Google Scholar 

  • Gross T (2010) Towards a new human-centred computing methodology for cooperative ambient intelligence. J Ambient Intell Humaniz Comput 1(1):31–42

    Article  MathSciNet  Google Scholar 

  • Hauert C, Monte S, Hofbauer J (2002) Volunteering as red queen mechanism for cooperation in public goods games. Science 296:1129–1132

    Article  Google Scholar 

  • Huang K, Wang T, Cheng Y (2015) Effect of heterogeneous investments on the evolution of cooperation in spatial public goods game. PLoS ONE 10:e0120317

    Article  Google Scholar 

  • Jiang W, Wang G, Zakirul Alam Bhuiyan Md, Wu J (2016) Understanding graph-based trust evaluation in online social networks: methodologies and challenges. ACM Comput Surv 49(1):10

    Article  Google Scholar 

  • Killingback T, Doebeli M, Hauert C (2010) Diversity of cooperation in the tragedy of the commons. Biol Theory 1:243–253

    Google Scholar 

  • Kohei M, Tanimoto J, Aya H (2013) Influence of stochastic perturbation of both action updating and strategy updating in mixed-strategy 2\(\times \)2 games on evolution of cooperation. Phys Rev E 88:062149

    Article  Google Scholar 

  • Kokubo S, Wang Z, Tanimoto J (2015) Spatial reciprocity for discrete, continuous and mixed strategy setups. Appl Math Comput 259:552–568

    MathSciNet  Google Scholar 

  • Lei C, Wu T, Jia JY (2010) Heterogeneity of allocation promotes cooperation in public goods games. Phys A Stat Mech Appl 389:4708–4714

    Article  Google Scholar 

  • Liang X, Xiao Y (2014) A survey of biological collaboration models. J Ambient Intell Humaniz Comput 5(4):551C563

    Article  Google Scholar 

  • Ma T, Zhou J, Tang M, Tian Y, Al-Dhelaan A, Al-Rodhaan M, Lee S (2015) Social network and tag sources based augmenting collaborative recommender system. IEICE Trans Inform Syst E98–D(4):902–910

    Article  Google Scholar 

  • Michael K, Friedrich B (2016) Risk sensitivity and assortment in social dilemmas. Soft Comput. doi:10.1007/s00500-016-2090-5

    Google Scholar 

  • Nax H, Perc M, Szolnoki A (2015) Stability of cooperation under image scoring in group interactions. Sci Rep 5:12145

  • Nowak M (2006) Five rules for the evolution of cooperation. Science 314:1560–1563

    Article  Google Scholar 

  • Nowak M, Sigmund K (1998) Evolution of indirect reciprocity by image scoring. Nature 393:573–577

    Article  Google Scholar 

  • Peng D, Yang H, Wang W (2010) Promotion of cooperation induced by nonuniform payoff allocation in spatial public goods game. Eur Phys J B 73:455–459

    Article  MATH  Google Scholar 

  • Perc M (2011) Success-driven distribution of public goods promotes cooperation but preserves defection. Phys Rev E 84:1915–1924

    Article  Google Scholar 

  • Rand D, Anna B, Tore E (2009) Positive interactions promote public cooperation. Science 325:1272–1275

    Article  MathSciNet  MATH  Google Scholar 

  • Ren Y, Li M, Sakurai K (2011) Finetrust: a fine-grained trust model for peer-to-peer networks. Secur Commun Netw 4(1):61–69

    Article  Google Scholar 

  • Ren Y, Li M, Xiang Y, Cui Y, Sakurai K (2013) Evolution of cooperation in reputation system by group-based scheme. J Supercomput 63(1):171–190

    Article  Google Scholar 

  • Ren Y, Shen J, Wang J, Han J, Lee S (2015) Mutual verifiable provable data auditing in public cloud storage. J Intern Technol 16(2):317–323

    Google Scholar 

  • Santos F, Santos M, Pacheco J (2008) Social diversity promotes the emergence of cooperation in public goods games. Nature 454:213–216

    Article  Google Scholar 

  • Schoenmakers S, Hilbe C, Blasius B (2014) Sanctions as honest signals—the evolution of pool punishment by public sanctioning institutions. J Theor Biol 356:1272–1275

    Article  MathSciNet  Google Scholar 

  • Shen J, Tan H, Wang J, Wang J, Lee S (2015) A novel routing protocol providing good transmission reliability in underwater sensor networks. J Intern Technol 16(1):171–177

    Google Scholar 

  • Smith J (1982) Evolution and the theory of games. Cambridge university press, Cambridge

    Book  MATH  Google Scholar 

  • Szolonki A, Perc M (2012) Evolutionary advantages of adaptive rewarding. New J Phys 14:93016–93029

    Article  Google Scholar 

  • Szolonki A, Perc M (2012) Conditional strategies and the evolution of cooperation in spatial public goods games. Phys Rev E 85:287–300

    Google Scholar 

  • Szolonki A, Perc M, Szab G (2009) Topology independent impact of noise on cooperation in spatial public goods games. Phys Rev E 80:2142–2152

    Google Scholar 

  • Szolonki A, Szab G, Perc M (2011) Phase diagrams for the spatial public goods game with pool punishment. Phys Rev E 83:856–875

    Google Scholar 

  • Szolonki A, Wang Z, Perc M (2012) Wisdom of groups promotes cooperation in evolutionary social dilemmas. Sci Rep 2:576

    Article  Google Scholar 

  • Tanimoto J (2015) Correlated asynchronous behavior updating with a mixed strategy system in spatial prisoner’s dilemma games enhances cooperation. Chaos Soliton Fract 80:39–46

    Article  MathSciNet  MATH  Google Scholar 

  • Teng X, Yan S, Tang S (2014) Individual behavior and social wealth in the spatial public goods game. Phys A Stat Mech Appl 402:141–149

    Article  MathSciNet  Google Scholar 

  • Tian L, Li M, Lu K (2013) The influence of age-driven investment on cooperation in spatial public goods games. Chaos Solitons Fract 54:65–70

    Article  MathSciNet  MATH  Google Scholar 

  • Vukov J, Santos F, Pacheco JM (2011) Escaping the tragedy of the commons via directed investments. J Theor Biol 287:37–41

    Article  MathSciNet  Google Scholar 

  • Wang Z, Szolonki A, Perc M (2012) Percolation threshold determines the optimal population density for public cooperation. Phys Rev E 85:922–938

    Google Scholar 

  • Xu B, Li M, Deng R (2015) The evolution of cooperation in spatial prisoner’s dilemma games with heterogeneous relationships. Phys A Stat Mech Appl 424:168–175

    Article  Google Scholar 

  • Yuan W, Xia C (2014) Role of investment heterogeneity in the cooperation on spatial public goods game. PLoS ONE 9:e91012

    Article  Google Scholar 

  • Zeng W, Li M, Chen F, Nan G (2016) Risk consideration and cooperation in the iterated prisoner’s dilemma. Soft Comput 20(2):567–587

    Article  Google Scholar 

  • Zhang H, Yang H, Du W (2010) Evolutionary public goods games on scale-free networks with unequal payoff allocation mechanism. Phys A Stat Mech Appl 389:1099–1104

    Article  Google Scholar 

  • Zhang H, Liu R, Wang Z (2012) Aspiration-induced reconnection in spatial public goods game. Europhys Lett 94:73–79

    Google Scholar 

  • Zhang J, Zhang C, Cao M (2015) How insurance affects altruistic provision in threshold public goods games. Sci Rep 5:9098

    Article  Google Scholar 

  • Zhong W, Kokubo S, Tanimoto J (2012) How is the equilibrium of continuous strategy game different from that of discrete strategy game. Biosystems 107:88–94

    Article  Google Scholar 

Download references

Acknowledgments

Authors like to appreciate the anonymous referees for their valuable comments and suggestions. This work is supported by the National Science Foundation of China (Grant Nos. 61100194, 61402141, 61100039, 61272173 and 61403059) and the Natural Science Foundation of Jiangsu Province (Grant No. BK20131277).

Author information

Authors and Affiliations

  1. School of Cyberspace, Hangzhou Dianzi University, Hangzhou, 310018, China

    Hong Ding, Yizhi Ren & Benyun Shi

  2. School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou, 310018, China

    Yao Zhang

  3. Key Laboratory of Complex Systems Modeling and Simulation, Ministry of Education, Hangzhou, China

    Hong Ding & Yizhi Ren

  4. Department of Information Systems and Cyber Security, University of Texas at San Antonio, San Antonio, TX, 78249-0631, USA

    Kim-Kwang Raymond Choo

  5. School of Information Technology and Mathematical Sciences, University of South Australia, Adelaide, SA, 5095, Australia

    Kim-Kwang Raymond Choo

Authors
  1. Hong Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yao Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yizhi Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Benyun Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Kim-Kwang Raymond Choo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Yizhi Ren or Benyun Shi.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Communicated by V. Loia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ding, H., Zhang, Y., Ren, Y. et al. Heterogeneous investment in spatial public goods game with mixed strategy. Soft Comput 22, 1287–1294 (2018). https://doi.org/10.1007/s00500-016-2415-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-016-2415-4

Keywords

Search

Navigation