In the cornout model two firms choose the amount of a product they wish to produce. It is assumed that the price that results is the market clearing price for the total supply. Is there a justification for this?
One way to interpret this result is to see our two-stage game as a mechanism to generate Cournot-like outcomes that dispenses with the mythical auctioneer.
A justification is given in Kreps-Scheinkmann (1983). They argue that this is the outcome if price competition follows production. For details see the linked article.