2 problems

Let $n\ge4$ be even. Let $\rho$ and $\phi$ be the game parameters, let $\pi_0$ and $b_{n-2}$ be the quantities defined for the stationary dynamics, and let $G_{n,n-2}$, $E_{n-2}$,…

Let $(\rho,\phi)$ be the parameters of the collective Parrondo game, and let the parameter plane be divided into the regions shown in Figure. For a finite word $w$ in the game symb…