I am trying to put forth a theory for endogenous supply chain formation. A set of $K$ complementary tasks need to be performed to manufacture a good $G$. If manufactured, there exists a demand function $d(p_G,q_G)$ that governs the price of the good in the market. Of the $K$ tasks involved in making the good, some are sequential and some are parallel (two complementary products combined to make one). In other words, there is a network (tree) structure that describes the ordering of the tasks.
Now let us assume there are $N>K$ firms in the market. If a firm decides to take up a task, it incurs some fixed cost for the plant, and some variable cost, depending on the number of units produced. However if altogether only a subset of the $K$ tasks are alone accomplished by the firms, then there is no good produced. Thus each firm's decision to produce is contingent on its wealth, its expected profit and the decisions of other firms.
My question: is there a similar theory for supply chain formation? I have read the following papers which come close to describing such formation but I find they are sufficiently different from what I have in mind.
- Ostrovsky, Michael. "Stability in supply chain networks." The American Economic Review (2008): 897-923.
- Corbett, Charles J., and Uday S. Karmarkar. "Competition and structure in serial supply chains with deterministic demand." Management Science 47.7 (2001): 966-978.
- Goyal, Sanjeev, and Fernando Vega-Redondo. "Structural holes in social networks." Journal of Economic Theory 137.1 (2007): 460-492.