Sequential Price Competition for Perfect Complements There are two goods, $1$ and $2$ produced by two firms at zero marginal costs. The goods are perfect complements. The demand for each goods is: $Q_1=Q_2=a-(p_1+p_2)$. The prices are set sequentially, with the leader firm ($1$) credibly committing to a price which the follower takes as given. Determine the equilibrium prices, quantities and profits. 


I understand that in standard Stackelberg games of prices, the follower has a second mover advantage. For the above question, I found that the reaction curves turned out to be downward sloping, i.e. prices are strategic substitutes. $(p^*_1,p^*_2)=(\frac{a}{2},\frac{a}{4})$. 
Would the second mover advantage still hold? Evaluating the leader's profit function at Bertrand prices would show that the leader has an incentive to set a price above $p^B_1$ since prices are strategic substitutes and goods are perfect complements (evaluating $\frac{\partial\pi_1^L}{\partial p_1}$ at bertrand prices). 
Is this the correct method to evaluate second mover/first mover advantage?
Just looking at the setup, everything is symmetric. This means that if they were to move simultaneously then we should have $p_1 = p_2$, and the payoffs for the two firms the same.

According to your calculation, $(p^*_1,p^*_2)=(\frac{a}{2},\frac{a}{4})$. Since $Q_1 = Q_2 \Rightarrow \pi_1 &gt; \pi_2$. So it's quite clear that in this case, the first mover has the advantage.

Intuitively, you can figure out which mover has the advantage by simply asking, would the first mover get higher payoff if he/she moves second?

Mathematically, if strategies are strategic substitute, then you can show that the first mover will have the advantage. Reference here.

Added later: one interesting way (I think) to look at this is this is just like Cournot competition, just with price and quantity switched.