Mistakes can stabilise the dynamics of rock-paper-scissors games
Fig 4
Various game transitions of the unstable RPS game as λ varies between [0, 1].
The components of the interior fixed point are plotted as functions of λ. 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). (A) The interior fixed point exists for all λ but vertices interchange their stability. In the limit of mistakes (λ → 0), two vertices are stable. (B) The interior fixed point exists for a sub-interval and vertices interchange their stability. As λ → 0, two vertices are stable. (C) The interior fixed point exists for two sub-intervals of (0, 1). In the limit of mistakes (λ → 0), only vertex 1 is stable. (D) The interior fixed point exists for almost all values of λ. In the limit of mistakes (λ → 0), all three vertices are stable. Generally, the exact equilibria transitions and existence of an interior equilibrium is determined by the limiting distribution of mistakes, S. We found that for almost all matrices S there is a high chance that at least one of the pure strategies will become dominant.