Handbook of Game Theory

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 $V_{\text{Π}}\left(t_k,p,q\right)$ be the value of the game starting at time $t_k$. One has $V_{\text{Π}}\left(1,p,q\right):=0$ and:

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