Abstract
The dynamics of how fair offers come about in ultimatum game is studied via the method of agent-based modeling. Both fairness motive and adaptive learning are considered to be important in the fair behavior of human players in concerning literature. Here special attention is paid to situations where adaptive learning proposers encounter responders with either pure money concern or fairness motivation. The simulation results show that the interplay of adaptive learning participants yields a perfect sub-game equilibrium, but fair offers will be provided by proposers as long as a small proportion of responders play “tough” against unfair offer.
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- 1.
Any strategy for the proposers combined with the strategy to accept the offer and reject all lower ones is counted as a Nash equilibrium, and a unique subgame perfect equilibrium. Strictly speaking, in discrete cases where the strategy choice includes zero, it counted as a subgame perfect equilibrium with the proposer offering either zero or the smallest possible divisible piece to the responder.
- 2.
In other words, we replace P1 with P1* that all agents’ exclusive motivation is to gain maximum amount of money except for some “tough” responders who follow a fairness motive and P3 with P3* that agents can identify his or her learning directions by comparing one’s latest payoffs.
- 3.
The reason why average demand of responders triumphs over average offer of proposers in the steady state is that some overly aspired responders keep random walking at a relatively high level as they turn down most offers.
References
Abbink K, Bolton GE, Sadrieh A, Tang FF (2001) Adaptive learning versus punishment in ultimatum bargaining. Games Econ Behav 37:1–25
Bolton GE (1991) A comparative model of bargaining: theory and evidence. Am Econ Rev 81:1096–1136
Bolton GE, Ockenfels A (2000) ERC: a theory of equity, reciprocity, and competition. Am Econ Rev 90:166–193
Brenner T, Vriend NJ (2006) On the behavior of proposers in ultimatum games. J Econ Behav Organ 61:617–631
Fehr E, Gachter S (1999) Cooperation and punishment in public goods experiments. Institute for Empirical Research in Economics working paper no. 10; CESifo working paper series no. 183
Fehr E, Schmidt KM (1999) A theory of fairness, competition, and cooperation. Q J Econ 114(3):817–868
Gittins JC (1979) Bandit processes and dynamic allocation indices. J R Stat Soc Ser B 41:148–177
Gittins JC (1989) Multi-armed bandit allocation indices. Wiley, Hoboken
Guth W, Schmittberger R, Schwarze B (1982) An experimental analysis of ultimatum bargaining. J Econ Behav Organ 3:367–388
Kirchsteiger G (1994) The role of envy in ultimatum games. J Econ Behav Organ 25:373–389
Nowak MA, Page KM, Sigmund K (2000) Fairness versus reason in the ultimatum game. Science 289(5485):1773–1775
Rabin M (1993) Incorporating fairness into game theory and economics. Am Econ Rev 83:1281–1302
Rand DG, Tarnita CE, Ohtsuki H et al (2013) Evolution of fairness in the one-shot anonymous ultimatum game. Proc Natl Acad Sci 110(7):2581–2586
Rotemberg JJ (2008) Minimally acceptable altruism and the ultimatum game. J Econ Behav Organ 66:457–476
Roth AE, Erev I (1995) Learning in extensive-form games: experimental data and simple dynamic models in the intermediate term. Games Econ Behav 8:164–212
Selten R, Stoecker R (1986) End behavior in sequences of finite prisoner’s dilemma supergames: a learning theory approach. J Econ Behav Organ 7:47–70
Thaler RH (1988) Anomalies: the ultimatum game. J Econ Perspect 2:195–206
Acknowledgements
We are grateful to Dr. Jianzhong Zhang for his suggestions and language improvements. This research was supported by National Natural Science Foundation of China under Grant of No. 61174165 and Program for New Century Excellent Talents in University (NCET-10-0245). This work was also the result of Interdisciplinary Salon of Beijing Normal University.
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Xiong, W., Fu, H., Wang, Y. (2014). Emergence of Fair Offers in Ultimatum Game. In: Leitner, S., Wall, F. (eds) Artificial Economics and Self Organization. Lecture Notes in Economics and Mathematical Systems, vol 669. Springer, Cham. https://doi.org/10.1007/978-3-319-00912-4_9
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