Dynamic Structure in a Four-strategy Game: Theory and Experiment

Wang Zhijian; Zhou Shujie; Yao Qinmei; Wang Yijia; Pan Gang

doi:10.21638/11701/spbu31.2022.26

Authors

Wang Zhijian Zhejiang University
Zhou Shujie Zhejiang University
Yao Qinmei Zhejiang University
Wang Yijia Ant Group
Pan Gang Zhejiang University

DOI:

https://doi.org/10.21638/11701/spbu31.2022.26

Abstract

Game dynamics theory, as any field of science, the consistency between theory and experiment is essential. In the past 10 years, important progress has been made in the merging of the theory and experiment in this field, in which dynamics cycle is the presentation. However, the achievement failed to eliminate the constraints of the Euclidean two-dimensional cycle. This paper uses a classic four-strategy game to study the dynamic structure (non-Euclidean superplane cycle). The consistency is in significant between the three ways: (1) analytical results from evolutionary dynamics equations, (2) agent-based simulation results from learning models and (3) laboratory results from human subjects game experiments. The consistency suggests that, the game dynamic structure could be quantitatively predictable, observable, and controllable in general.

Keywords:

game theory, laboratory game experiment, eigenvector, eigenmode, dynamics system theory

Downloads

Download data is not yet available.

References

Binmore, K., Swierzbinski, J. and Proulx, C. (2001). Does minimax work? an experimental study. Economic Journal, 111(473), 445–464

Camerer, C. (2003). Behavioral game theory: Experiments in strategic interaction. Princeton University Press

Cason, T. N., Daniel, F. and Hopkins, E. D. (2014). Cycles and instability in a rock-paper-scissors population game: A continuous time experiment. Review of Economic Studies, 81(1), 112–136

Cason, T. N., Friedman, D. and Hopkins, E. (2010). Testing the tasp: An experimental investigation of learning in games with unstable equilibria. Journal of Economic Theory, 145(6), 2309–2331

Cason, T. N., Friedman, D. and Hopkins, E. (2021). An experimental investigation of price dispersion and cycles. Journal of Political Economy, 129(3), 789–841

Friedman, D. and Sinervo, B. (2016). Evolutionary games in natural, social, and virtual worlds. Oxford University Press

Hofbauer, J., Sigmund, K., et al. (1998). Evolutionary games and population dynamics. Cambridge university press

Iyetomi, H., Aoyama, H., Fujiwara, Y., Souma, W., Vodenska, I. and Yoshikawa, H. (2020). Relationship between macroeconomic indicators and economic cycles in us. Scientific reports, 10(1), 1–12

Izquierdo, L. R., Izquierdo, S. S. and Sandholm, W. H. (2019). An introduction to abed: Agent-based simulation of evolutionary game dynamics. Games and Economic Behavior, 118, 434–462

Okano, Y. (2013). Minimax play by team. Games & Economic Behavior

O'Neill, B. (1987). Nonmetric test of the minimax theory of two-person zerosum games. Proceedings of the National Academy of Sciences

Roussel, M. R. (2019). Invariant manifolds. In Nonlinear Dynamics, pp. 6-1–6-20. Morgan & Claypool Publishers

Sandholm, W. H. (2010). Population Games and Evolutionary Dynamics. MIT Press

Schoonbeek, L. (1987). On the eigenvectors of macro-economic models. Annales d'Economie et de Statistique, 6–7, 335–345

Taylor, P. D. and Jonker, L. B. (1978). Evolutionary stable strategies and game dynamics. Mathematical biosciences, 40(1–2), 145–156

Van Huyck, J., Rankin, F. and Battalio, R. (1999). What does it take to eliminate the use of a strategy strictly dominated by a mixture? Experimental economics, 2(2), 129–150

Wang, Z. (2022). Game dynamics structure control by design: an example from experimental economics. arXiv preprint arXiv:2203.06088

Wang, Y., Chen, X. and Wang, Z. (2017). Testability of evolutionary game dynamics based on experimental economics data. Physica A: Statistical Mechanics and its Applications, 486, 455–464

Wang, Z., Xu, B. and Zhou, H.-J. (2014). Social cycling and conditional responses in the rock-paper-scissors game. Scientific reports, 4(1), 1–7

Wang, Z. and Yao, Q. (2020). Human social cycling spectrum. arXiv preprint arXiv:2012.03315

Xu, B., Wang, S., and Wang, Z. (2014). Periodic frequencies of the cycles in 2×2 games: evidence from experimental economics. European Physical Journal B, 87(2), 46

Yao, Q. (2021). Theoretical analysis and experiment of dynamic structure of high dimensional game. Available at: https://cdmd.cnki.com.cn/Article/CDMD-10335-1021626407.htm, https://doi.org/10.27461/d.cnki.gzjdx.2021.000847 (accessed 22.08.2022)

Zhou, S. (2021). Theory and experiment of dynamic structure in four strategy game. Available at: https://cdmd.cnki.com.cn/Article/CDMD-10335-1021626406.htm (accessed 22.08.2022); https://doi.org/10.27461/d.cnki.gzjdx.2021.000844