I've been working on some problems related to Bayesian games, and I reached this dynamic game that I have been having some problems with. Consider a game where a polar bear and panda bear are choosing to fight or not fight. The polar bear knows whether he is soft or tough, but the panda knows that the polar bear is soft or tough with probabilities $\frac{1}{7}$ and $\frac{6}{7}$ respectively. The Polar Bear has the choice to stay on the ice ($I$) or go to land ($L$). The Panda Bear observes this action, but does not observe whether the Polar Bear is soft or tough. The panda can choose to fight the Polar Bear ($Fi$) or ignore it by eating bamboo ($B$). If the Panda chooses to fight, the Panda gets a payoff of $-3$ if the Polar Bear is tough and $1$ if the Polar Bear is soft. If the Panda stays eating bamboo, the panda will earn $0$. If the Polar Bear is soft, the Polar Bear obtains a payoff of $-2$ in the case that the Panda fights and $1$ if the Panda stays eating bamboo. If the Polar Bear is tough, the Polar Bear earns a payoff of $0$ if the Panda Fights and $1$ if the Panda stays eating bamboo. Moreover, the Polar Bear must face a cost $c_{PB} > 0$ if the Polar Bear goes on land ($L$).
I'm interested in figuring out the conditions on $c_{PB}$ in order to guarantee the existence of a "separating" Perfect Bayesian Equilibrium. Any suggestions on how to go about this kind of problem?