Join Up or Stay Away? Coalition Formation for Critical IT Infrastructure

We consider districts that invest in critical IT infrastructure, which spill over to other districts. IT infrastructure is considered critical if its disruption can cause significant damage to security, the economy, public health, or safety. Districts choose whether to participate in a coalition noncooperatively, and the coalition subsequently makes resource investment decisions cooperatively. Districts "inside" the coalition have superior interoperability in the spillovers relative to "outside" districts. Inside districts also benefit from a coalition economy of scale and a discounted resource investment cost, and they face diseconomies of scope in the number of coalition members and their investment levels. Coalition structures include grand, partial (varying in size), minimal (two members), and singleton, and we consider the formation of only one coalition. We find that inside districts' resource levels decrease with coalition size. Even with homogeneous districts, any size coalition can be an equilibrium depending on the coalition economy of scale and the relative interoperability of resources in inside versus outside districts. The equilibrium coalition size is increasing in the economy of scale and decreasing in relative interoperability. Similarly, any size coalition can be socially optimal depending on the coalition economy of scale and relative interoperability. The socially optimal coalition size is also increasing in the economy of scale and decreasing in relative interoperability. In most cases, the socially optimal coalition size is larger than the equilibrium coalition. A subsidy or tax can incentivize the equilibrium coalition size and district resource levels to be socially optimal, providing a general solution to the provisioning of critical IT infrastructure. We use the European Union's Digital COVID Certificate program providing vaccine status information and the U.S. Government's Direct Project that supports the establishment of nationwide health information exchanges to illustrate elements of our model.