Intermediate Case of Bertrand and Cournot I am wondering whether there is a model of oligopolies in which we have some intermediate case of Bertrand and Cournot competition. What I do not mean by "intermediate" is the mixed Bertrand - Cournot game in which one firm sets a price and the other sets a quantity. What I also do not mean (I think) is monopolistic competition in which goods are not perfect substitutes.

Rather, I mean a model in which there are degrees of commitment to prices and quantities. For example, a cookie producer can softly commit to a cookie amount by only purchasing a certain number of ovens and softly commit to a price by printing the price on the cookie boxes. At some extra cost, it is however possible to later scramble to rent an extra oven or to reprint price labels. I am wondering whether this has been modeled anywhere. Ideal would be a parametric version with the parameter indicating whether we are in the pure Bertrand or in the Cournot case.
These papers could be interesting to you. First, a classical contribution:
Singh Nirvikar and Xavier Vives, 1984. "Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of Economics, vol. 15(4), pages 546-554.
And these two interesting papers, using the concept of competition toughness to reconcile Cournot and Bertrand:
d'Aspremont, Claude &amp; Dos Santos Ferreira, Rodolphe, 2009. "Price-quantity competition with varying toughness," Games and Economic Behavior, 65, 62-82.
d'Aspremont Claude and Rodolphe Dos Santos Ferreira &amp; Louis-André Gérard-Varet, 2007. "Competition For Market Share Or For Market Size: Oligopolistic Equilibria With Varying Competitive Toughness," International Economic Review, 48, 761-784.