Autonomous Agents and Multi-Agent Systems

, Volume 22, Issue 1, pp 103–126 | Cite as

Human-inspired computational fairness

  • Steven de Jong
  • Karl Tuyls
Open Access


In many common tasks for multi-agent systems, assuming individually rational agents leads to inferior solutions. Numerous researchers found that fairness needs to be considered in addition to individual reward, and proposed valuable computational models of fairness. In this paper, we argue that there are two opportunities for improvement. First, existing models are not specifically tailored to addressing a class of tasks named social dilemmas, even though such tasks are quite common in the context of multi-agent systems. Second, the models generally rely on the assumption that all agents will and can adhere to these models, which is not always the case. We therefore present a novel computational model, i.e., human-inspired computational fairness. Upon being confronted with social dilemmas, humans may apply a number of fully decentralized sanctioning mechanisms to ensure that optimal, fair solutions emerge, even though some participants may be deciding purely on the basis of individual reward. In this paper, we show how these human mechanisms may be computationally modelled, such that fair and optimal solutions emerge from agents being confronted with social dilemmas.


Multi-agent systems Reinforcement learning Fairness Human-inspired mechanisms Social dilemmas 


  1. 1.
    Aldewereld, H. (2007). Autonomy vs. conformity: An institutional perspective on norms and protocols. PhD thesis, Universiteit Utrecht.Google Scholar
  2. 2.
    Axelrod R. (1984) The evolution of cooperation. Basic Books, New YorkGoogle Scholar
  3. 3.
    Barabasi A.-L., Albert R. (1999) Emergence of scaling in random networks. Science 286: 509–512CrossRefMathSciNetGoogle Scholar
  4. 4.
    Basu K. (1994) The traveler’s dilemma: Paradoxes of rationality in game theory. American Economic Review 84(2): 391–395Google Scholar
  5. 5.
    Bearden, J. N. (2001). Ultimatum bargaining experiments: The state of the art. SSRN eLibrary.Google Scholar
  6. 6.
    Binmore K. G. (1991) Fun and games: A text on game theory. D.C. Heath, LexingtonGoogle Scholar
  7. 7.
    Bourke T. (2001) Server load balancing. O’Reilly Media Inc, SebastopolGoogle Scholar
  8. 8.
    Boyd R., Gintis H., Bowles S., Richerson P. J. (2003) The evolution of altruistic punishment. Proceedings of the National Academy of Science USA 100: 3531–3535CrossRefGoogle Scholar
  9. 9.
    Chevaleyre Y., Dunne P., Endriss U., Lang J., Lemaître M., Maudet N., Padget J., Phelps S., Rodriguez-Aguilar J., Sousa P. (2006) Issues in multiagent resource allocation. Informatica 30: 3–31zbMATHGoogle Scholar
  10. 10.
    Chevaleyre, Y., Endriss, U., Lang, J., & Maudet, N. (2007). A short introduction to computational social choice. In Proceedings of the 33rd conference on current trends in theory and practice of computer science (SOFSEM-2007), Vol. 4362 of LNCS (pp. 51–69). Berlin: Springer.Google Scholar
  11. 11.
    Dall’Asta L., Baronchelli A., Barrat A., Loreto V. (2006) Agreement dynamics on small-world networks. Europhysics Letters 73(6): 969–975CrossRefMathSciNetGoogle Scholar
  12. 12.
    Dannenberg, A., Riechmann, T., Sturm, B., & Vogt, C. (2007). Inequity aversion and individual behavior in public good games: An experimental investigation. SSRN eLibrary.Google Scholar
  13. 13.
    de Jong, S. (2009). Fairness in multi-agent systems. PhD thesis, Maastricht University.Google Scholar
  14. 14.
    de Jong, S., & Tuyls, K. (2008). Learning to cooperate in public-goods interactions 2008. Presented at the EUMAS’08 Workshop, Bath, UK, December 18–19.Google Scholar
  15. 15.
    de Jong, S., & Tuyls, K. (2009). Learning to cooperate in a continuous tragedy of the commons. In Proceedings of the 8th International Conference on Autonomous Agents and Multi-Agent Systems (AAMAS 2009) (pp. 1185–1186).Google Scholar
  16. 16.
    de Jong, S., Tuyls, K., & Verbeeck, K. (2008a). Artificial agents learning human fairness. In Proceedings of the International Joint Conference on Autonomous Agents and Multi-Agent Systems (AAMAS’08) (pp. 863–870).Google Scholar
  17. 17.
    de Jong S., Tuyls K., Verbeeck K. (2008b) Fairness in multi-agent systems. Knowledge Engineering Review 23(2): 153–180Google Scholar
  18. 18.
    de Jong S., Tuyls K., Verbeeck K., Roos N. (2008) Priority awareness: Towards a computational model of human fairness for multi-agent systems. Adaptive Agents and Multi-Agent Systems III. Adaptation and Multi-Agent Learning 4865: 117–128CrossRefGoogle Scholar
  19. 19.
    de Jong S., Uyttendaele S., Tuyls K. (2008) Learning to reach agreement in a continuous ultimatum game. Journal of Artificial Intelligence Research 33: 551–574zbMATHMathSciNetGoogle Scholar
  20. 20.
    Endriss, U. (2008). Fair division. Tutorial at the International Conference on Autonomous Agents and Multi-Agent Systems (AAMAS).Google Scholar
  21. 21.
    Endriss, U., Maudet, N., Sadri, F., & Toni, F. (2003). On optimal outcomes of negotiations over resources. In: AAMAS ’03: Proceedings of the Second International Joint Conference on Autonomous Agents and Multiagent Systems (pp. 177–184). New York: ACM. ISBN 1-58113-683-8. doi: 10.1145/860575.860604.
  22. 22.
    Endriss U., Maudet N., Sadri F., Toni F. (2006) Negotiating socially optimal allocations of resources. Journal of Artificial Intelligence Research 25: 315–348MathSciNetGoogle Scholar
  23. 23.
    Fehr E., Gaechter S. (2002) Altruistic punishment in humans. Nature 415: 137–140CrossRefGoogle Scholar
  24. 24.
    Fehr E., Schmidt K. (1999) A theory of fairness, competition and cooperation. Quarterly Journal of Economics 114: 817–868zbMATHCrossRefGoogle Scholar
  25. 25.
    Gerding E., van Bragt D., Poutré J. L. (2003) Multi-issue negotiation processes by evolutionary simulation: Validation and social extensions. Computational Economics 22: 39–63zbMATHCrossRefGoogle Scholar
  26. 26.
    Gintis H. (2001) Game theory evolving: A problem-centered introduction to modeling strategic interaction. Princeton University Press, PrincetonGoogle Scholar
  27. 27.
    Gueth W., Schmittberger R., Schwarze B. (1982) An experimental analysis of ultimatum bargaining. Journal of Economic Behavior and Organization 3(4): 367–388CrossRefGoogle Scholar
  28. 28.
    Hardin G. (1968) The tragedy of the commons. Science 162: 1243–1248CrossRefGoogle Scholar
  29. 29.
    Hauert C., Monte S. D., Hofbauer J., Sigmund K. (2002) Volunteering as red queen mechanism for cooperation in public goods games. Science 296: 1129–1132CrossRefGoogle Scholar
  30. 30.
    Hennes, D. (2008). Multi-agent learning in stochastic games—Piecewise and state-coupled replicator dynamics. Master’s thesis, Universiteit Maastricht.Google Scholar
  31. 31.
    Henrich J., Boyd R., Bowles S., Camerer C., Fehr E., Gintis H. (2004) Foundations of human sociality: Economic experiments and ethnographic evidence from fifteen small-scale societies. Oxford University Press, OxfordGoogle Scholar
  32. 32.
    Kalagnanam J., Parkes D. C. (2004) Auctions, bidding and exchange design. In: Simchi-Levi D., Wu S. D., Shen M. (eds) Handbook of quantitative supply chain analysis: Modeling in the e-business era, Int. Series in operations research and management science, Chapter 5. Kluwer, Dordrecht, pp 1–84Google Scholar
  33. 33.
    Kollock P. (1998) Social dilemmas: The anatomy of cooperation. Annual Review of Sociology 24: 183–214CrossRefGoogle Scholar
  34. 34.
    Larrick R., Blount S. (1997) The claiming effect: Why players are more generous in social dilemmas than in ultimatum games. Journal of Personality and Social Psychology 72(4): 810–825CrossRefGoogle Scholar
  35. 35.
    Messick D. M., Brewer M. B. (1983) Solving social dilemmas: A review. Review of Personality and Social Psychology 4: 11–44Google Scholar
  36. 36.
    Milinski M., Semmann D., Krambeck H. J. (2002) Reputation helps solve the tragedy of the commons. Nature 415: 424–426CrossRefGoogle Scholar
  37. 37.
    Nowak M. A., Page K. M., Sigmund K. (2000) Fairness versus reason in the ultimatum game. Science 289: 1773–1775CrossRefGoogle Scholar
  38. 38.
    Oosterbeek H., Sloof R., van de Kuilen G. (2004) Cultural differences in ultimatum game experiments: Evidence from a meta-analysis. Experimental Economics 7: 171–188zbMATHCrossRefGoogle Scholar
  39. 39.
    Panchanathan K., Boyd R. (2004) Indirect reciprocity can stabilize cooperation without the second-order free rider problem. Nature 432: 499–502CrossRefGoogle Scholar
  40. 40.
    Rockenbach, B., & Milinski, M. (2006). The efficient interaction of indirect reciprocity and costly punishment. Nature, 444(7120), 718–723. ISSN 0028-0836.Google Scholar
  41. 41.
    Russell S., Norvig P. (2003) Artificial intelligence: A modern approach (2nd ed.). Prentice-Hall, Englewood CliffsGoogle Scholar
  42. 42.
    Sandholm, T. (2006). Optimal winner determination algorithms. In P. Cramton, Y. Shoham, & R. Steinberg (Eds.), Combinatorial auctions, Chapter 14. MIT Press.Google Scholar
  43. 43.
    Santos F. C., Pacheco J. M. (2005) Scale-free networks provide a unifying framework for the emergence of cooperation. Physical Review Letters 95: 98–104Google Scholar
  44. 44.
    Santos F. C., Pacheco J. M., Lenaerts T. (2006) Cooperation prevails when individuals adjust their social ties. PLoS Computational Biology 2(10): 1284–1291CrossRefGoogle Scholar
  45. 45.
    Sen A. K. (1970) Collective choice and social welfare. Holden Day, San FranciscozbMATHGoogle Scholar
  46. 46.
    Shoham Y., Powers R., Grenager T. (2007) If multi-agent learning is the answer, what is the question?. Artificial Intelligence 171(7): 365–377zbMATHCrossRefMathSciNetGoogle Scholar
  47. 47.
    Sigmund K., Hauert C., Nowak M. A. (2001) Reward and punishment. Proceedings of the National Academy of Sciences 98(19): 10757–10762CrossRefGoogle Scholar
  48. 48.
    Sutton R.S., Barto A.G. (1998) Reinforcement learning: An introduction. MIT Press. A Bradford Book, Cambridge, MAGoogle Scholar
  49. 49.
    Thathachar M. A. L., Sastry P. S. (2004) Networks of learning automata: Techniques for online stochastic optimization. Kluwer, DordrechtGoogle Scholar
  50. 50.
    Tuyls K., Nowé A. (2005) Evolutionary game theory and multi-agent reinforcement learning. The Knowledge Engineering Review 20: 63–90CrossRefGoogle Scholar
  51. 51.
    Tuyls, K., & Westra, R. (2009). Replicator dynamics in discrete and continuous strategy spaces. In Accepted in multi-agent systems: Simulation and applications (accepted).Google Scholar
  52. 52.
    Uyttendaele, S. (2008). Fairness and agreement in complex networks. Master’s thesis, MICC, Maastricht University.Google Scholar
  53. 53.
    Verbeeck K., Nowé A., Parent J., Tuyls K. (2007) Exploring selfish reinforcement learning in repeated games with stochastic rewards. Journal of Autonomous Agents and Multi-Agent Systems 14: 239–269CrossRefGoogle Scholar
  54. 54.
    Yamagishi T. (1986) The provision of a sanctioning system as a public good. Journal of Personality and Social Psychology 51(1): 110–116CrossRefGoogle Scholar
  55. 55.
    Zimmermann M. G., Eguíluz V. M. (2005) Cooperation, social networks, and the emergence of leadership in a prisoner’s dilemma with adaptive local interactions. Physical Review E 72(5): 056118. doi: 10.1103/PhysRevE.72.056118 CrossRefMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Computational Modelling LabVrije Universiteit BrusselBrusselsBelgium
  2. 2.Department of Knowledge EngineeringMaastricht UniversityMaastrichtThe Netherlands

Personalised recommendations