Skip to main content

Dynamics of Fairness in Groups of Autonomous Learning Agents

  • Conference paper
  • First Online:
Autonomous Agents and Multiagent Systems (AAMAS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10002))

Included in the following conference series:

Abstract

Fairness plays a determinant role in human decisions and definitely shapes social preferences. This is evident when groups of individuals need to divide a given resource. Notwithstanding, computational models seeking to capture the origins and effects of human fairness often assume the simpler case of two person interactions. Here we study a multiplayer extension of the well-known Ultimatum Game. This game allows us to study fair behaviors in a group setting: a proposal is made to a group of Responders and the overall acceptance depends on reaching a minimum number of individual acceptances. In order to capture the effects of different group environments on the human propensity to be fair, we model a population of learning agents interacting through the multiplayer ultimatum game. We show that, contrarily to what would happen with fully rational agents, learning agents coordinate their behavior into different strategies, depending on factors such as the minimum number of accepting Responders (to achieve group acceptance) or the group size. Overall, our simulations show that stringent group criteria leverage fairer proposals. We find these conclusions robust to (i) asynchronous and synchronous strategy updates, (ii) initially biased agents, (iii) different group payoff division paradigms and (iv) a wide range of error and forgetting rates.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bloembergen, D., Tuyls, K., Hennes, D., Kaisers, M.: Evolutionary dynamics of multi-agent learning: a survey. J. Artif. Intell. Res. 53, 659–697 (2015)

    MathSciNet  MATH  Google Scholar 

  2. Blount, S.: When social outcomes aren’t fair: the effect of causal attributions on preferences. Organ. Behav. Hum. Decis. Process. 63(2), 131–144 (1995)

    Article  Google Scholar 

  3. Bornstein, G., Yaniv, I.: Individual and group behavior in the ultimatum game: are groups more rational players? Exp. Econ. 1(1), 101–108 (1998)

    Article  MATH  Google Scholar 

  4. Cimini, G., Sánchez, A.: Learning dynamics explains human behaviour in prisoner’s dilemma on networks. J. R. Soc. Interface 11(94), 20131186 (2014)

    Article  Google Scholar 

  5. de Melo, C.M., Carnevale, P., Gratch, J.: The effect of expression of anger and happiness in computer agents on negotiations with humans. In: The 10th International Conference on Autonomous Agents and Multiagent Systems, International Foundation for Autonomous Agents and Multiagent Systems, pp. 937–944 (2011)

    Google Scholar 

  6. Duch, R., Przepiorka, W., Stevenson, R.: Responsibility attribution for collective decision makers. Am. J. Polit. Sci. 59(2), 372–389 (2015)

    Article  Google Scholar 

  7. Elbittar, A., Gomberg, A., Sour, L.: Group decision-making and voting in ultimatum bargaining: an experimental study. B.E. J. Econ. Anal. Policy 11(1), 53 (2011)

    Google Scholar 

  8. Erev, I., Roth, A.E.: Predicting how people play games: reinforcement learning in experimental games with unique, mixed strategy equilibria. Am. Econ. Rev. 88, 848–881 (1998)

    Google Scholar 

  9. Fischbacher, U., Fong, C.M., Fehr, E.: Fairness, errors and the power of competition. J. Econ. Behav. Organ. 72(1), 527–545 (2009)

    Article  Google Scholar 

  10. Forsythe, R., Horowitz, J.L., Savin, N.E., Sefton, M.: Fairness in simple bargaining experiments. Games Econ. Behav. 6(3), 347–369 (1994)

    Article  MATH  Google Scholar 

  11. Fudenberg, D., Levine, D.K.: The Theory of Learning in Games. MIT press, Cambridge (1998)

    MATH  Google Scholar 

  12. Grosskopf, B.: Reinforcement and directional learning in the ultimatum game with responder competition. Exp. Econ. 6(2), 141–158 (2003)

    Article  MATH  Google Scholar 

  13. Güth, W., Schmittberger, R., Schwarze, B.: An experimental analysis of ultimatum bargaining. J. Econ. Behav. Organ. 3(4), 367–388 (1982)

    Article  Google Scholar 

  14. Hagan, J.D., Everts, P.P., Fukui, H., Stempel, J.D.: Foreign policy by coalition: deadlock, compromise, and anarchy. Int. Stud. Rev. 3(2), 169–216 (2001)

    Article  Google Scholar 

  15. Hamilton, W.D.: Innate social aptitudes of man: an approach from evolutionary genetics. In: Fox, R. (ed.) Biosocial Anthropology, pp. 133–155. Wiley, New York (1975)

    Google Scholar 

  16. Hoffman, E., McCabe, K., Smith, V.L.: Social distance and other-regarding behavior in dictator games. Am. Econ. Rev. 86, 653–660 (1996)

    Google Scholar 

  17. Iranzo, J., Román, J., Sánchez, A.: The spatial ultimatum game revisited. J. Theor. Biol. 278(1), 1–10 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. Jennings, N.R., Faratin, P., Lomuscio, A.R., Parsons, S., Wooldridge, M.J., Sierra, C.: Automated negotiation: prospects, methods and challenges. Group Decis. Negot. 10(2), 199–215 (2001)

    Article  Google Scholar 

  19. Jing, X., Xie, J.: Group buying: a new mechanism for selling through social interactions. Manage. Sci. 57(8), 1354–1372 (2011)

    Article  MATH  Google Scholar 

  20. Kauffman, R.J., Lai, H., Ho, C.-T.: Incentive mechanisms, fairness and participation in online group-buying auctions. Electron. Commer. Res. Appl. 9(3), 249–262 (2010)

    Article  Google Scholar 

  21. Lin, R., Kraus, S.: Can automated agents proficiently negotiate with humans? Commun. ACM 53(1), 78–88 (2010)

    Article  Google Scholar 

  22. Macy, M.W., Flache, A.: Learning dynamics in social dilemmas. Proc. Natl. Acad. Sci. 99, 7229–7236 (2002)

    Article  Google Scholar 

  23. Messick, D.M., Moore, D.A., Bazerman, M.H.: Ultimatum bargaining with a group: underestimating the importance of the decision rule. Organ. Behav. Hum. Decis. Process. 69(2), 87–101 (1997)

    Article  Google Scholar 

  24. Newell, A., Rosenbloom, P.S.: Mechanisms of skill acquisition and the law of practice. Cogn. Skills Acquisition 1, 1–55 (1981)

    Google Scholar 

  25. Nowak, M.A., Page, K.M., Sigmund, K.: Fairness versus reason in the ultimatum game. Science 289(5485), 1773–1775 (2000)

    Article  Google Scholar 

  26. Oosterbeek, H., Sloof, R., Van De Kuilen, G.: Cultural differences in ultimatum game experiments: evidence from a meta-analysis. Exp. Econ. 7(2), 171–188 (2004)

    Article  MATH  Google Scholar 

  27. Osborne, M.J.: An Introduction to Game Theory. Oxford University Press, New York (2004)

    Google Scholar 

  28. Pacheco, J.M., Santos, F.C., Souza, M.O., Skyrms, B.: Evolutionary dynamics of collective action. In: Chalub, F.A.C.C., Rodrigues, J.F. (eds.) The Mathematics of Darwin’s Legacy, pp. 119–138. Springer, Basel (2011)

    Chapter  Google Scholar 

  29. Page, K.M., Nowak, M.A.: Empathy leads to fairness. Bull. Math. Biol. 64(6), 1101–1116 (2002)

    Article  MATH  Google Scholar 

  30. Page, K.M., Nowak, M.A., Sigmund, K.: The spatial ultimatum game. Proc. R. Soc. Lond. B Biol. Sci. 267(1458), 2177–2182 (2000)

    Article  Google Scholar 

  31. Pinheiro, F.L., Santos, M.D., Santos, F.C., Pacheco, J.M.: Origin of peer influence in social networks. Phys. Rev. Lett. 112(9), 098702 (2014)

    Article  Google Scholar 

  32. Rand, D.G., Tarnita, C.E., Ohtsuki, H., Nowak, M.A.: Evolution of fairness in the one-shot anonymous ultimatum game. Proc. Natl. Acad. Sci. 110(7), 2581–2586 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  33. Rendell, L., Boyd, R., Cownden, D., Enquist, M., Eriksson, K., Feldman, M.W., Fogarty, L., Ghirlanda, S., Lillicrap, T., Laland, K.N.: Why copy others? insights from the social learning strategies tournament. Science 328(5975), 208–213 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  34. Rosenfeld, A., Zuckerman, I., Segal-Halevi, E., Drein, O., Kraus, S.: Negochat-a: a chat-based negotiation agent with bounded rationality. Auton. Agent. Multi-Agent Syst. 30(1), 60–81 (2016)

    Article  Google Scholar 

  35. Roth, A.E., Erev, I.: Learning in extensive-form games: experimental data and simple dynamic models in the intermediate term. Games Econ. Behav. 8(1), 164–212 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  36. Santos, F.P., Santos, F.C., Melo, F.S., Paiva, A., Pacheco, J.M.: Learning to be fair in multiplayer ultimatum games. In: Proceedings of the 2016 International Conference on Autonomous Agents and Multiagent Systems, International Foundation for Autonomous Agents and Multiagent Systems, pp. 1381–1382 (2016)

    Google Scholar 

  37. Santos, F.P., Santos, F.C., Paiva, A.: The evolutionary perks of being irrational. In: Proceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems, International Foundation for Autonomous Agents and Multiagent Systems, pp. 1847–1848 (2015)

    Google Scholar 

  38. Santos, F.P., Santos, F.C., Paiva, A., Pacheco, J.M.: Evolutionary dynamics of group fairness. J. Theor. Biol. 378, 96–102 (2015)

    Article  MATH  Google Scholar 

  39. Segal-Halevi, E., Hassidim, A., Aumann, Y.: Waste makes haste: bounded time protocols for envy-free cake cutting with free disposal. In: Proceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems, International Foundation for Autonomous Agents and Multiagent Systems, pp. 901–908 (2015)

    Google Scholar 

  40. Sequeira, P., Melo, F.S., Paiva, A.: Emergence of emotional appraisal signals in reinforcement learning agents. Auton. Agents Multi-Agent Syst. 29(4), 537–568 (2014)

    Article  Google Scholar 

  41. Sigmund, K.: The Calculus of Selfishness. Princeton University Press, Princeton (2010)

    Book  MATH  Google Scholar 

  42. Sinatra, R., Iranzo, J., Gomez-Gardenes, J., Floria, L.M., Latora, V., Moreno, Y.: The ultimatum game in complex networks. J. Stat. Mech. Theory Exp. 2009(09), P09012 (2009)

    Article  Google Scholar 

  43. Skyrms, B.: Signals: Evolution, Learning, and Information. Oxford University Press, Oxford (2010)

    Book  Google Scholar 

  44. Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction. MIT Press, Cambridge (1998)

    Google Scholar 

  45. Szolnoki, A., Perc, M., Szabó, G.: Defense mechanisms of empathetic players in the spatial ultimatum game. Phys. Rev. Lett. 109(7), 078701 (2012)

    Article  Google Scholar 

  46. Thaler, R.H.: Anomalies: the ultimatum game. J. Econ. Perspect. 2, 195–206 (1988)

    Article  Google Scholar 

  47. Thorndike, E.L.: Animal intelligence: an experimental study of the associative processes in animals. In: The Psychological Review: Monograph Supplements, (4), i (1898)

    Google Scholar 

  48. Van Segbroeck, S., De Jong, S., Nowé, A., Santos, F.C., Lenaerts, T.: Learning to coordinate in complex networks. Adapt. Behav. 18(5), 416–427 (2010)

    Article  Google Scholar 

  49. Van Segbroeck, S., Pacheco, J.M., Lenaerts, T., Santos, F.C.: Emergence of fairness in repeated group interactions. Phys. Rev. Lett. 108(15), 158104 (2012)

    Article  Google Scholar 

  50. Weibull, J.W.: Evolutionary Game Theory. MIT Press, Cambridge (1997)

    MATH  Google Scholar 

Download references

Acknowledgments

This research was supported by Fundação para a Ciência e Tecnologia (FCT Portugal) through grants SFRH/BD/94736/2013, PTDC/EEI-SII/5081/2014, PTDC/MAT/STA/3358/2014 and by multi-annual funding of CBMA and INESC-ID (under the projects UID/BIA/04050/2013 and UID/CEC/50021/2013 provided by FCT).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fernando P. Santos .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing AG

About this paper

Cite this paper

Santos, F.P., Santos, F.C., Melo, F.S., Paiva, A., Pacheco, J.M. (2016). Dynamics of Fairness in Groups of Autonomous Learning Agents. In: Osman, N., Sierra, C. (eds) Autonomous Agents and Multiagent Systems. AAMAS 2016. Lecture Notes in Computer Science(), vol 10002. Springer, Cham. https://doi.org/10.1007/978-3-319-46882-2_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-46882-2_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46881-5

  • Online ISBN: 978-3-319-46882-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics