In-house capacity investment and outsourcing under competition

We analyze a two buyer-one supplier setting. The buyers first simultaneously invest in in-house capacity with the knowledge of the demand distribution only. The demand is then realized after the investments are made. If the demand exceeds the invested capacity then, the balance requirement is sourced by the buyers from a common supplier. The supplier has the option to sell its capacity to an alternate market (where demand is random) and to these two buyers. We determine the equilibrium capacity investments by the two buyers in the presence of a supplier who has an alternate market.