#### 2.3.4.2 General RG and viscosity tools

We follow Cardaliaguet et al. (2012).

(A) RG with incomplete information. Consider an arbitrarily evaluation probability μ on $\mathbb{N}*$ inducing a partition Π. Let ${V}_{\text{\Pi}}\left({t}_{k},p,q\right)$ be the value of the game starting at time ${t}_{k}$. One has ${V}_{\text{\Pi}}\left(1,p,q\right):=0$ and:

${V}_{\text{\Pi}}\left({t}_{n},p,q\right)=\text{val}\left[{\mu}_{n+1}g\left(x,y,p,q\right)+{\displaystyle \sum _{i,j}x\left(i\right)y\left(j\right){V}_{\text{\Pi}}\left({t}_{n+1},p\left(i\right),q\left(i\right)\right)}\right].$