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Social Learning in the Ultimatum Game

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  • Boyu Zhang

Abstract

In the ultimatum game, two players divide a sum of money. The proposer suggests how to split and the responder can accept or reject. If the suggestion is rejected, both players get nothing. The rational solution is that the responder accepts even the smallest offer but humans prefer fair share. In this paper, we study the ultimatum game by a learning-mutation process based on quantal response equilibrium, where players are assumed boundedly rational and make mistakes when estimating the payoffs of strategies. Social learning is never stabilized at the fair outcome or the rational outcome, but leads to oscillations from offering 40 percent to 50 percent. To be precise, there is a clear tendency to increase the mean offer if it is lower than 40 percent, but will decrease when it reaches the fair offer. If mutations occur rarely, fair behavior is favored in the limit of local mutation. If mutation rate is sufficiently high, fairness can evolve for both local mutation and global mutation.

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  • Boyu Zhang, 2013. "Social Learning in the Ultimatum Game," PLOS ONE, Public Library of Science, vol. 8(9), pages 1-6, September.
    • Handle: RePEc:plo:pone00:0074540
    DOI: 10.1371/journal.pone.0074540
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    2. Kang, Kai & Tian, Jinyan & Zhang, Boyu, 2024. "Cooperation and control in asymmetric repeated games," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    3. Yanling Zhang & Feng Fu, 2018. "Strategy intervention for the evolution of fairness," PLOS ONE, Public Library of Science, vol. 13(5), pages 1-13, May.
    4. Antonios Avgeris & Panagiota Sergaki & Achilleas Kontogeorgos & Antonios Tiganis, 2020. "Reciprocity in Student Groups: Experimental Evidence from Greece," International Journal of Economic Sciences, International Institute of Social and Economic Sciences, vol. 9(1), pages 44-67, June.
    5. Zhang, Boyu, 2016. "Quantal response methods for equilibrium selection in normal form games," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 113-123.
    6. Ramzi Suleiman, 2017. "Economic Harmony: An Epistemic Theory of Economic Interactions," Games, MDPI, vol. 8(1), pages 1-15, January.

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