Trust is at the core of a decentralized system.
Simply put, one needs to know that someone working in another location or without direct oversight will complete whatever they say they will do and take responsibility for it. When people are given the space to create and solve problems on their own, then the expectation is that they will do just that.
Leadership and oversight of people working in a decentralized company works well when there is a clear vision for the future and a set of values to support it. Employees and other members of the system need to know what you stand for, and this will in turn guide them as they make their own decisions about what's best for their customers.
When information flows unencumbered between people in a decentralized organization, then it is easier to know what is happening in the various parts of your company. The role of the leader in this situation is to remove barriers to progress so that people can focus specifically on getting work done. Communication needs to flow freely in all directions.
A loosely organized, but tightly focused group of people can be very effective and it's not unlike what you see in corporate research and development offices, military special forces, and companies that are spread over a large geographic area. Various digital tools now exist that make it very easy for people to stay in touch and collaborate on projects.
When done well, people get used to working in a way where they feel appreciated and respected and, most importantly, they feel that they are able to express themselves creatively through their work. Building a culture of creative problem solving starts with giving people room to make their own decisions--and being there to assist when they do need guidance. When this system is working well, this enables your entire team to be very adaptable, flexible, and ready for any kind of problem that may come their way.
A networked culture of creative problem solvers sounds like a mouthful, but this what leaders now have at their disposal. The challenge for leaders and managers is to figure out how to harness their power--and it starts with trust.