Three duopolists operate in a market with inverse demand given by p$($Q$)=$a$-$q$,$ where Q$=$q$1+$q$2+$q$3$ and qi is the quantity produced by firm i$.$ Each firm has a constant marginal cost of production, c$,$ and no fixed cost. The firms choose their quantities as follows: $(1)$ firm $1$ chooses q$1$; $(2)$ firms $2$ and $3$ observe q$1$ and then simultaneously choose q$2$ and q$3,$ respectively.