Research Paper:
Evolutionary Competition in Small-Size Lowest Unique Integer Games
Takashi Yamada
Yamaguchi University
1677-1 Yoshida, Yamaguchi-shi, Yamaguchi 753-8541, Japan
In lowest unique integer games (LUIGs), continually choosing the same number has been experimentally and computationally shown to be effective. However, this result holds only when all players behave differently, and it is unclear whether such behavior performs well under population dynamics. This study analyzed the types of agents that survive and how successfully they behave within an evolutionary environment of small-size LUIGs. Here, the author identified a learning model to create agents using behavioral data obtained from a laboratory experiment by Yamada and Hanaki. Then, evolutionary competition was pursued. The main findings are three fold. First, more agents are ruled out in three-person LUIGs than in four-person LUIGs. Second, the most successful agents do not win as much as the generations increase. Instead, they manage to win by adaptively changing their strategies. Third, as the scale of the LUIG increases, the number of wins for each agent is not correlated with that in a round-robin contest.
- [1] T. Yamada and N. Hanaki, “An Experiment on Lowest Unique Integer Games,” Physica A: Statistical Mechanics and its Applications, Vol.463, pp. 88-102, 2016. https://doi.org/10.1016/j.physa.2016.06.108
- [2] R. Östling, J. T.-y. Wang, E. Y. Chou, and C. F. Camerer, “Testing Game Theory in the Field: Swedish LUPI Lottery Games,” American Economic J.: Microeconomics, Vol.3, No.3, pp. 1-33, 2011.
- [3] T. Yamada, “Behavioral Heterogeneity Affects Individual Performances in Experimental and Computational Lowest Unique Integer Games,” Frontiers in Physics, Vol.5, 2017. https://doi.org/10.3389/fphy.2017.00065
- [4] P. Dal Bó and G. R. Fréchette, “The Evolution of Cooperation in Infinitely Repeated Games: Experimental Evidence,” Vol.101, No.1, pp. 411-429, 2011. https://doi.org/10.1257/aer.101.1.411
- [5] D. Fudenberg, D. G. Rand, and A. Dreber, “Slow to Anger and Fast to Forgive: Cooperation in an Uncertain World,” American Economic Review, Vol.102, No.2, pp. 720-749, 2012. https://doi.org/10.1257/aer.102.2.720
- [6] J. Juul, A. Kianercy, S. Bernhardsson, and S. Pigolotti, “Replicator Dynamics with Turnover of Players,” Physical Review E, Vol.88, Issue 2, Article No.022806, 2013. https://doi.org/10.1103/PhysRevE.88.022806
- [7] J. Linde, J. Sonnemans, and J. Tuinstra, “Strategies and Evolution in the Minority Game: A Multi-Round Strategy Experiment,” Games and Economic Behavior, Vol.86, pp. 77-95, 2014. https://doi.org/10.1016/j.geb.2014.03.001
- [8] R. Axelrod, “The Complexity of Cooperation: Agent-Based Models of Competition and Collaboration,” Princeton University Press, 1997.
- [9] K. Binmore, “The Complexity of Cooperation: Agent-Based Models of Competition and Collaboration,” J. of Artificial Societies and Social Simulation, Vol.1, No.1, 1998.
- [10] B. Linster, “Evolutionary Stability in the Infinitely Repeated Prisoners’ Dilemma Played by Two-State Moore Machines,” Southern Economic J., Vol.58, No.4, pp. 880-903, 1992. https://doi.org/10.2307/1060227
- [11] J. Duffy, “Agent-Based Models and Human Subject Experiments,” L. Tesfatsion and K. L. Judd (Eds.), “Handbook of Computational Economics,” Vol.2, pp. 949-1011, 2006. https://doi.org/10.1016/S1574-0021(05)02019-8
- [12] C. F. Camerer, “Behavioral Game Theory: Experiments in Strategic Interaction,” Russell Sage Foundation, 1997.
- [13] I. Erev and A. E. Roth, “Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria,” The American Economic Review, Vol.88, No.4, pp. 848-881, 1998.
- [14] E. Mohlin, R. Östling, and J. T.-y. Wang, “Learning by Similarity-Weighted Imitation in Winner-Takes-All Games,” Games and Economic Behavior, Vol.120, pp. 225-245, 2020. https://doi.org/10.1016/j.geb.2019.12.008
- [15] E. Mohlin, R. Östling, and J. T.-y. Wang, “Lowest Unique Bid Auctions with Population Uncertainty,” Economics Letters, Vol.134, pp. 53-57, 2015. https://doi.org/10.1016/j.econlet.2015.06.009
- [16] Y. Raviv and G. Virag, “Gambling by Auctions,” Int. J. of Industrial Organization, Vol.27, Issue 3, pp. 369-378, 2009.
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