A game of rock-paper-scissors is an interesting example of an interaction where none of the pure strategies strictly dominates all others, leading to a cyclic pattern. In this work, we consider an unstable version of rock-paper-scissors dynamics and allow individuals to make behavioural mistakes during the strategy execution. We show that such an assumption can break a cyclic relationship leading to a stable equilibrium emerging with only one strategy surviving. We consider two cases: completely random mistakes when individuals have no bias towards any strategy and a general form of mistakes. Then, we determine conditions for a strategy to dominate all other strategies. However, given that individuals who adopt a dominating strategy are still prone to behavioural mistakes in the observed behaviour, we may still observe extinct strategies. That is, behavioural mistakes in strategy execution stabilise evolutionary dynamics leading to an evolutionary stable and, potentially, mixed co-existence equilibrium.
PLoS Computational Biology
Authors would like to thank Christian Hilbe and Martin Nowak for their inspiring and very helpful feedback on the manuscript.
Kleshnina M, Streipert SS, Filar JA, Chatterjee K. Mistakes can stabilise the dynamics of rock-paper-scissors games. PLoS Computational Biology. 2021;17(4). doi:10.1371/journal.pcbi.1008523
Kleshnina, M., Streipert, S. S., Filar, J. A., & Chatterjee, K. (2021). Mistakes can stabilise the dynamics of rock-paper-scissors games. PLoS Computational Biology. https://doi.org/10.1371/journal.pcbi.1008523
Kleshnina, Maria, Sabrina S. Streipert, Jerzy A. Filar, and Krishnendu Chatterjee. “Mistakes Can Stabilise the Dynamics of Rock-Paper-Scissors Games.” PLoS Computational Biology, 2021. https://doi.org/10.1371/journal.pcbi.1008523.
M. Kleshnina, S. S. Streipert, J. A. Filar, and K. Chatterjee, “Mistakes can stabilise the dynamics of rock-paper-scissors games,” PLoS Computational Biology, vol. 17, no. 4. 2021.
Kleshnina M, Streipert SS, Filar JA, Chatterjee K. 2021. Mistakes can stabilise the dynamics of rock-paper-scissors games. PLoS Computational Biology. 17(4), e1008523.
Kleshnina, Maria, et al. “Mistakes Can Stabilise the Dynamics of Rock-Paper-Scissors Games.” PLoS Computational Biology, vol. 17, no. 4, e1008523, 2021, doi:10.1371/journal.pcbi.1008523.
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