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.