Abstract
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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Axelrod R, Hamilton W D. The evolution of cooperation. Science, 1981, 211: 1390–1396
Milinski M. Tit for tat in sticklebacks and the evolution of cooperation. Nature, 1987, 325: 433–435
Colman A M. Game Theory and Its Applications in the Social and Biological Sciences. Oxford: Butterworth-Heinemann, 1995
Dugatkin L A. Cooperation Among Animals: An Evolutionary Perspective. Oxford: Oxford University Press, 1997
West S A, Pen I, Griffin A S. Cooperation and competition between relatives. Science, 2002, 296: 72–75
Hauert C, Szabó G. Prisoner’s dilemma and public goods games in different geometries: Compulsory versus voluntary interactions. Complexity, 2003, 8: 31–38
Archetti M. The volunteer’s dilemma and the optimal size of a social group. J Theor Biol, 2009, 261: 475–480
Nikiforakis N, Normann H T, Wallace B. Asymmetric enforcement of cooperation in a social dilemma. S Econ J, 2010, 76: 638–659
Axelrod R. The Evolution of Cooperation. New York: Basic Books, 1984
Frank S A. Foundations of Social Evolution Princeton. New Jersey: Princeton University Press, 1998
West S A, Griffin A S, Gardner A. Social semantics: Altruism, cooperation, mutualism, strong reciprocity and group selection. J Evol Biol, 2007, 20: 415–432
Diekmann A. Volunteer’s dilemma. J Confl Resol, 1985, 29: 605–610
Darley J M, Latane B. Bystander intervention in emergencies: Diffusion of responsibility. J Pers Soc Psychol, 1968, 8: 377–383
Otsubo H, Rapoport A. Dynamic volunteer’s dilemmas over a finite horizon-An experimental study. J Confl Resol, 2008, 52: 961–984
Pellmyr O, Huth C J. Evolutionary stability of mutualism between yuccas and yucca moths. Nature, 1994, 372: 257–260
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: e7802
Wang R W, Sun B F, Zheng Q. Diffusive co-evolution and mutualism maintenance mechanisms in a fig-fig wasp system. Ecology, 2010, 91: 1308–1316
Archetti M. Cooperation as a volunteer’s dilemma and the strategy of conflict in public goods games. J Evol Biol, 2009, 22: 2192–2200
Diekmann A. Cooperation in an asymmetric volunteer’s dilemma game theory and experimental evidence. Int J Game Theory, 1993, 22: 75–85
Ratnieks F L W, Wenseleers T. Altruism in insect societies and beyond: Voluntary or enforced? Trends Ecol Evol, 2008, 23: 45–52
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: 1487–1496
Healy A, Pate J. Asymmetry and incomplete information in an experimental volunteer’s dilemma. 18th World IMACS/MODSIM Congress, Cairns, Australia, 2009. 1457–1462
Reeve H K. Queen activation of lazy workers in colonies of the eusocial naked mole-rat. Nature, 1992, 358: 147–149
Heinsohn R, Packer C. Complex cooperative strategies in group-territorial African lions. Science, 1995, 269: 1260–1262
Wang R W, Shi L. The evolution of cooperation in asymmetric systems. Sci China Life Sci, 2010, 53: 139–149
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: 1041–1046
Harsanyi J C, Slten R. A General Theory of Equilibrium Selection in Games. Cambridge, MA: MIT Press, 1988
Binmore K G. Playing Fair: Game Theory and the Social Contract. Cambridge, MA: MIT Press, 1994
Oster G F, Wilson E O. Caste and Ecology in the Social Insects. Princeton, NJ: Princeton University Press, 1978
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: 2545–2552
Frank S A. Policing and group cohesion when resources vary. Anim Behav, 1996, 52: 1163–1169
Ratnieks F L W, Wenseleers T. Policing insect societies. Science, 2005, 307: 54–56
Ratnieks F L W, Visscher P K. Worker policing in honeybees. Nature, 1989, 342: 796–797
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: 268–273
Halling L A, Oldroyd B P, Wattanachaiyingcharoen W, et al. Worker policing in the bee Apis florae. Behav Ecol Sociobiol, 2001, 49: 509–513
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: 1427–1434
Wenseleers T, Ratnieks F L W. Comparative analysis of worker reproduction and policing in eusocial hymenoptera supports relatedness theory. Am Nat, 2006, 168: 163–179
Duchateau M J. Agonistic behaviour in colonies of the bumblebee Bombus terrestris. J Ethol, 1989, 7: 141–151
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: 1339–1344
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: 4486–4491
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: 2460–2464
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: 758–767
Hollén L I, Radford A N. The development of alarm call behaviour in mammals and birds. Anim Behav, 2009, 78: 791–800
Bronstein J L. The costs of mutualism. Am Zool, 2001, 41: 825–839
Boyd R, Richerson P J. The evolution of reciprocity in sizeable groups. J Theor Biol, 1988, 132: 337–356
Weesie J. Asymmetry and timing in the volunteer’s dilemma. J Confl Resol, 1993, 37: 569–590
Weesie J, Franzen A. Cost sharing in a volunteer’s dilemma. J Confl Resol, 1998, 42: 600–618
Author information
Authors and Affiliations
Corresponding authors
Additional information
These authors contributed equally to this work.
This article is published with open access at Springerlink.com
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
He, J., Wang, R., Christopher, X.J.J. et al. Cooperation in an asymmetric volunteer’s dilemma game with relatedness. Chin. Sci. Bull. 57, 1972–1981 (2012). https://doi.org/10.1007/s11434-012-5178-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11434-012-5178-z