We consider the models of sequential games over supply chain networks and production chain networks. In the supply chain model, we show that in particular, for series-parallel networks, there is a unique equilibrium.

We provide a polynomial time algorithm to compute the equilibrium and study the impact of the network structure to the total trade flow at equilibrium. Our results shed light on the trade-off between competition, production cost, and double marginalization.

In the production chain model, we investigated sequential decisions and delegation options over three agents, chain, and tree networks. Our main contribution is showing the value of delegation and how to maximumly leverage the middleman's aligned interests with the principal. In particular, we provide a polynomial time algorithm to find the optimal delegation structure and the corresponding necessary contract payments for the principal. Furthermore, we analyzed the trade-off of the delegation and gave a deeper insight into the value of delegation in different conditions. Several questions are left for future research such as what's the optimal delegation structures in general tree and how to build the model that agents can try multiple times until the task is successful.