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Mistakes can stabilise the dynamics of rock-paper-scissors games
Fig 3
Game transitions under execution errors from example 2.
(A) Frequencies of each strategies in the interior equilibrium as functions of λ. Here, x1 represents rock frequency, x2—paper frequency and x3—scissors frequency. The interior equilibrium exists for most the values of λ but (
, 
). Further, the coloured bar at the top of the plot indicates stability intervals of λ for different vertices (a stable vertex is indicated on top of the bar). For instance, vertex 3 is the only stable vertex for λ ∈ (≈ 0.287, 
). Game flow for the unstable rock-paper-scissors game is depicted for different values of λ as follows: (B) λ = 1, (C) λ = 0.3, (D) λ = 0.27, (E) λ = 0.22, (F) λ = 0.205, (G) λ = 0.16, (H) λ = 0.1, (I) λ = 0.05, (J) λ = 0. We depicted each transition in the game from panel A. Here, a stable fixed point is denoted by a red circle and a unstable fixed point is denoted by a white circle. Hence, as λ changes its values from 1 to 0, the game experiences several transitions in its equilibria and for different degrees of execution errors, each of the pure strategies has a chance to dominate. However, for the maximum plasticity, only pure rock strategy survives.
doi: https://doi.org/10.1371/journal.pcbi.1008523.g003