Partial compatibility under ATM networks

Matutes and Padilla study the incentives of banks to share their Automatic Teller Machines (ATMs) when they are competitors in the market for deposit. They show that full compatibility never constitutes a Perfect Coalition-Proof Nash equilibrium in pure strategy. Only full incompatibility or partial compatibility occurs. In order to explain why at least two banks would be willing to share their ATMs but not to remain incompatible, they set up some conditions. One of these conditions is the range of the loan rate. The paper follows the structure of Matutes and Padilla, but the solution for the range of the loan rate is different from the one in Matutes and Padilla's model.