DSE 2010 Question 58: Monopolistic competition and oligopoly

Consider a Bertrand duopoly with firms 1 and 2 producing a homogeneous good and setting prices $p_{1},p_{2}$ that must be positive integers. If $p_{1}<p_{2}$ (resp. $p_{1}>p_{2}$), firm 1 (resp. firm 2) sells $5-p_{1}$ (resp. $5-p_{2}$) and the other sells nothing; if $p_{1}=p_{2}$, each sells $(5-p_{1})/2$. Firm 1 has constant average cost $5/2$ and firm 2 has constant average cost $3/2$. In equilibrium