I have a question regarding the below situation
Alice and Bob are two partners in a joint project. Simultaneously, Alice and Bob put efforts $e_A$ and $e_B \in [0,1]$ respectively, to the project, and the project succeeds with probability $e_A^{1/2}e_B^{1/2}$. The payoffs of Alice and Bob are $\theta_A-e_A^2$ and $\theta_B-e_B^2$, respectively, if the project succeeds; the payoffs are $-e_A^2$ and $-e_B^2$ otherwise. Here, $\theta_A$ and $\theta_B$ are privately known by Alice and Bob, and respectively, and they are independently and uniformly distributed on $[0,1]$.
How can I represent this game as a Bayesian game and determine a symmetric Nash equilibrium in increasing strategies ?