How, precisely, does local competition reduce security?
Two security organizations are competing for your business. You pick A as your provider. B now has an incentive to reduce your security (either actively or passively) in order to show you the error of your choice.
This is destabilizing at the interaction boundaries between security providers.
If B actively attempts to reduce your security, then that is an attack on you, and it would necessarily be defended by A. Both A and B have incentive to avoid this: War is expensive. So, all things being equal, and A and B acting rationally, this would not happen.
If B passively attempts to reduce your security, for instance, ignoring a break-in or mugging, they pass up an opportunity to prove themselves more capable of providing you security than A, to say nothing of the chance to present A with a bill for services rendered. So B, therefore, has incentive not to do that, either.
If anything, local competition would increase the security provided, not decrease.
And yet the borderlands are where the trouble always starts...
The problem for the consumer is that there is some tacit level of cooperation between A and B. Unless the security violation by A is above a certain threshold B will not be willing to incur the cost of dealing with it. The territorial ambitions of China in the Philippine Sea is an excellent example of this. Fishermen from the wrong security provider are experiencing losses due to theft by fishermen from the right security provider. The various involved security providers are unwilling to escalate beyond a certain point. Fishermen have reduced security.
No. Have not read referenced book. How does it explain the Parcel islands and Falkland Islands security situations?