Chinese Science Bulletin

, Volume 57, Issue 16, pp 1972–1981 | Cite as

Cooperation in an asymmetric volunteer’s dilemma game with relatedness

  • JunZhou He
  • RuiWu WangEmail author
  • X. J. Jensen Christopher
  • YaoTang LiEmail author
  • ChaoQian Li
Open Access
Article Ecology


What motivates some members of a social group to voluntarily incur costs in order to provide for the common good? This question lies at the heart of theoretical and empirical studies of cooperative behavior. This is also the question that underlies the classic volunteer’s dilemma model, which has been previously explored in scenarios where group members are related or interact asymmetrically. Here we present a model that combines asymmetry and relatedness, showing that the probability of volunteerism in such systems depends closely on both the degree of asymmetry and level of relatedness between interacting individuals. As has been shown in previous volunteer’s dilemma models, the payoff ratio and overall group size also influence the probability of volunteerism. The probability of volunteerism decreases with increasing group size or decreasing cost-to-benefit ratio of the co-players; in the presence of asymmetrical interactions, subordinate players were more likely to offer public goods than the dominant player. More asymmetrical interactions decrease the probability of volunteerism of the dominant player; overall volunteerism increases with increasing relatedness.


asymmetric interaction cooperation volunteer’s dilemma relatedness public goods kin selection inclusive fitness 


  1. 1.
    Axelrod R, Hamilton W D. The evolution of cooperation. Science, 1981, 211: 1390–1396CrossRefGoogle Scholar
  2. 2.
    Milinski M. Tit for tat in sticklebacks and the evolution of cooperation. Nature, 1987, 325: 433–435CrossRefGoogle Scholar
  3. 3.
    Colman A M. Game Theory and Its Applications in the Social and Biological Sciences. Oxford: Butterworth-Heinemann, 1995Google Scholar
  4. 4.
    Dugatkin L A. Cooperation Among Animals: An Evolutionary Perspective. Oxford: Oxford University Press, 1997Google Scholar
  5. 5.
    West S A, Pen I, Griffin A S. Cooperation and competition between relatives. Science, 2002, 296: 72–75CrossRefGoogle Scholar
  6. 6.
    Hauert C, Szabó G. Prisoner’s dilemma and public goods games in different geometries: Compulsory versus voluntary interactions. Complexity, 2003, 8: 31–38CrossRefGoogle Scholar
  7. 7.
    Archetti M. The volunteer’s dilemma and the optimal size of a social group. J Theor Biol, 2009, 261: 475–480CrossRefGoogle Scholar
  8. 8.
    Nikiforakis N, Normann H T, Wallace B. Asymmetric enforcement of cooperation in a social dilemma. S Econ J, 2010, 76: 638–659Google Scholar
  9. 9.
    Axelrod R. The Evolution of Cooperation. New York: Basic Books, 1984Google Scholar
  10. 10.
    Frank S A. Foundations of Social Evolution Princeton. New Jersey: Princeton University Press, 1998Google Scholar
  11. 11.
    West S A, Griffin A S, Gardner A. Social semantics: Altruism, cooperation, mutualism, strong reciprocity and group selection. J Evol Biol, 2007, 20: 415–432CrossRefGoogle Scholar
  12. 12.
    Diekmann A. Volunteer’s dilemma. J Confl Resol, 1985, 29: 605–610CrossRefGoogle Scholar
  13. 13.
    Darley J M, Latane B. Bystander intervention in emergencies: Diffusion of responsibility. J Pers Soc Psychol, 1968, 8: 377–383CrossRefGoogle Scholar
  14. 14.
    Otsubo H, Rapoport A. Dynamic volunteer’s dilemmas over a finite horizon-An experimental study. J Confl Resol, 2008, 52: 961–984CrossRefGoogle Scholar
  15. 15.
    Pellmyr O, Huth C J. Evolutionary stability of mutualism between yuccas and yucca moths. Nature, 1994, 372: 257–260CrossRefGoogle Scholar
  16. 16.
    Wang R W, Ridley J, Sun B F, et al. Interference competition and high temperatures reduce the virulence of fig wasps and stabilize a fig-wasp mutualism. PLoS ONE, 2009, 4: e7802CrossRefGoogle Scholar
  17. 17.
    Wang R W, Sun B F, Zheng Q. Diffusive co-evolution and mutualism maintenance mechanisms in a fig-fig wasp system. Ecology, 2010, 91: 1308–1316CrossRefGoogle Scholar
  18. 18.
    Archetti M. Cooperation as a volunteer’s dilemma and the strategy of conflict in public goods games. J Evol Biol, 2009, 22: 2192–2200CrossRefGoogle Scholar
  19. 19.
    Diekmann A. Cooperation in an asymmetric volunteer’s dilemma game theory and experimental evidence. Int J Game Theory, 1993, 22: 75–85CrossRefGoogle Scholar
  20. 20.
    Ratnieks F L W, Wenseleers T. Altruism in insect societies and beyond: Voluntary or enforced? Trends Ecol Evol, 2008, 23: 45–52CrossRefGoogle Scholar
  21. 21.
    Wang R W, Sun B F, Zheng Q, et al. Asymmetric interaction and indeterminate fitness correlation between cooperative partners in the fig-fig wasp mutualism. J R Soc Interface, 2011, 8: 1487–1496CrossRefGoogle Scholar
  22. 22.
    Healy A, Pate J. Asymmetry and incomplete information in an experimental volunteer’s dilemma. 18th World IMACS/MODSIM Congress, Cairns, Australia, 2009. 1457–1462Google Scholar
  23. 23.
    Reeve H K. Queen activation of lazy workers in colonies of the eusocial naked mole-rat. Nature, 1992, 358: 147–149CrossRefGoogle Scholar
  24. 24.
    Heinsohn R, Packer C. Complex cooperative strategies in group-territorial African lions. Science, 1995, 269: 1260–1262CrossRefGoogle Scholar
  25. 25.
    Wang R W, Shi L. The evolution of cooperation in asymmetric systems. Sci China Life Sci, 2010, 53: 139–149CrossRefGoogle Scholar
  26. 26.
    Wang R W, He J Z, Wang Y Q, et al. Asymmetric interaction will facilitate the evolution of cooperation. Sci China Life Sci, 2010, 53: 1041–1046CrossRefGoogle Scholar
  27. 27.
    Harsanyi J C, Slten R. A General Theory of Equilibrium Selection in Games. Cambridge, MA: MIT Press, 1988Google Scholar
  28. 28.
    Binmore K G. Playing Fair: Game Theory and the Social Contract. Cambridge, MA: MIT Press, 1994Google Scholar
  29. 29.
    Oster G F, Wilson E O. Caste and Ecology in the Social Insects. Princeton, NJ: Princeton University Press, 1978Google Scholar
  30. 30.
    Shi L, Wang R W, Zhu L X, et al. Varying coefficient analysis for indeterminate species interactions with non-parametric estimation, exemplifying with a fig-fig wasp system. Chin Sci Bull, 2011, 56: 2545–2552CrossRefGoogle Scholar
  31. 31.
    Frank S A. Policing and group cohesion when resources vary. Anim Behav, 1996, 52: 1163–1169CrossRefGoogle Scholar
  32. 32.
    Ratnieks F L W, Wenseleers T. Policing insect societies. Science, 2005, 307: 54–56CrossRefGoogle Scholar
  33. 33.
    Ratnieks F L W, Visscher P K. Worker policing in honeybees. Nature, 1989, 342: 796–797CrossRefGoogle Scholar
  34. 34.
    Oldroyd B P, Ratnieks F L W. Anarchistic honey bee workers evade worker policing by laying eggs that have low remove rates. Behav Ecol Sociobiol, 2000, 47: 268–273CrossRefGoogle Scholar
  35. 35.
    Halling L A, Oldroyd B P, Wattanachaiyingcharoen W, et al. Worker policing in the bee Apis florae. Behav Ecol Sociobiol, 2001, 49: 509–513CrossRefGoogle Scholar
  36. 36.
    D’Ettorre P, Heinze J, Ratnieks F L W. Worker policing by egg eating in the ponerine ant Pachycondyla inversa. Proc R Soc Lond B, 2004, 271: 1427–1434CrossRefGoogle Scholar
  37. 37.
    Wenseleers T, Ratnieks F L W. Comparative analysis of worker reproduction and policing in eusocial hymenoptera supports relatedness theory. Am Nat, 2006, 168: 163–179CrossRefGoogle Scholar
  38. 38.
    Duchateau M J. Agonistic behaviour in colonies of the bumblebee Bombus terrestris. J Ethol, 1989, 7: 141–151CrossRefGoogle Scholar
  39. 39.
    Liebig J, Monnin T, Turillazzi S. Direct assessment of queen quality and lack of worker suppression in a paper wasp. Proc R Soc B, 2005, 272: 1339–1344CrossRefGoogle Scholar
  40. 40.
    Keeling C I, Slessor K N, Higo H A, et al. New components of the honey bee (Apis mellifera L.) queen retinue pheromone. Proc Natl Acad Sci USA, 2003, 100: 4486–4491CrossRefGoogle Scholar
  41. 41.
    Beggs K T, Glendining K A, Marechal N M, et al. Queen pheromone modulates brain dopamine function in worker honey bees. Proc Natl Acad Sci USA, 2007, 104: 2460–2464CrossRefGoogle Scholar
  42. 42.
    Hollén L I, Manser M B. Motivation before meaning: Motivational information encoded in meerkat alarm calls develops earlier than referential information. Am Nat, 2007, 169: 758–767CrossRefGoogle Scholar
  43. 43.
    Hollén L I, Radford A N. The development of alarm call behaviour in mammals and birds. Anim Behav, 2009, 78: 791–800CrossRefGoogle Scholar
  44. 44.
    Bronstein J L. The costs of mutualism. Am Zool, 2001, 41: 825–839CrossRefGoogle Scholar
  45. 45.
    Boyd R, Richerson P J. The evolution of reciprocity in sizeable groups. J Theor Biol, 1988, 132: 337–356CrossRefGoogle Scholar
  46. 46.
    Weesie J. Asymmetry and timing in the volunteer’s dilemma. J Confl Resol, 1993, 37: 569–590CrossRefGoogle Scholar
  47. 47.
    Weesie J, Franzen A. Cost sharing in a volunteer’s dilemma. J Confl Resol, 1998, 42: 600–618CrossRefGoogle Scholar

Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsYunnan UniversityKunmingChina
  2. 2.State Key Laboratory of Genetic Resources and Evolution, Kunming Institute of ZoologyChinese Academy of SciencesKunmingChina
  3. 3.Department of Mathematics and Science, School of Liberal Arts and SciencesPratt InstituteBrooklynUSA

Personalised recommendations