Handbook of Game Theory

2.6.3 Quantitative Differential Games with Incomplete Information

An approach similar to the one for RG has been introduced by Cardaliaguet (2007) and developed by Cardaliaguet and Rainer (2009a) to study differential games of fixed duration with incomplete information. Stochastic differential games with incomplete information have been analyzed by Cardaliaguet and Rainer (2009a) (see also Buckdahn et al., 2010).

The model works as follows. Let K and L be two finite sets. For each (k,ℓ), a differential game ${\text{Γ}}^{kl}$ on [0, T] with control sets U and V is given. The initial position of the system is $z_0=\left\{z_0^{kl}\right\}\in Z^{K\times L}$, the dynamics is $f^{kl}\left(z^{kl},t,u,v\right)$