Perfect Bayesian Equilibria
Hint:
You can convert the game into the following normal form:
\begin{equation}
\begin{array}{|c|c|c|}
\hline
&amp; Steal &amp; Split \\\hline 
Steal &amp; 100\beta, 0&amp; 100(1-\alpha),0 \\\hline 
Split &amp; 50(\alpha+\beta),50+50(1-\alpha-\beta) &amp; 50,50 \\\hline
\end{array}
\end{equation}
Note that Steal is a weakly dominant strategy for player 2, so (Split, Split) can never be an equilibrium.