Dynamics of Fairness in Groups of Autonomous Learning Agents
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.
KeywordsNash Equilibrium Multiagent System Artificial Agent Ultimatum Game Strategy Profile
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).
- 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
- 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
- 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
- 24.Newell, A., Rosenbloom, P.S.: Mechanisms of skill acquisition and the law of practice. Cogn. Skills Acquisition 1, 1–55 (1981)Google Scholar
- 27.Osborne, M.J.: An Introduction to Game Theory. Oxford University Press, New York (2004)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
- 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
- 44.Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction. MIT Press, Cambridge (1998)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