Free banks compete, as it were, on an even playing field in issuing paper IOUs, which are basically what banknotes are. They have to redeem those IOUs on a regular basis: The competition among different issuers means that their notes will be treated the same way that checks are treated by banks today. They will be accumulated for a day or so and then sent through the clearing system for collection. It's this competition among issuers that assures that none of them has the power to lead the system into a general overexpansion.
Later, when asked about the prospects for free banking in the United States, Selgin answers,
Financial innovations tend to take us in the direction of free banking. Such innovations have already privatized the greater part of national money stocks, and will keep doing so in the absence of a wholesale nationalization of banks. It's only currency and coin that private firms have long been prevented from supplying.
So long as private currency remains illegal, and even if it doesn't, further financial innovation will tend to make us less and less dependent on any sort of paper currency or coins. Smart cards, debit cards, that sort of thing, have already made some inroads. And global pressures tend to favor the loosening of other kinds of bank regulations. There is, however, one kind of regulation that is growing instead of retreating and that market forces can't or won't resist, namely, government guarantees.
I would like to see this whole issue analyzed in terms of signaling. With free banking, I suspect that we would get cyclical movements in the perceived soundness of banks. People would grow to trust the signals of at least some banks more and more, until those banks abuse that trust. Then, when people lose money, the trust will drop way off.
The same thing happens under regulated banking, of course. Which is where those government guarantees come in.
The question I have is whether a system of government guarantees produces an overall higher level of economic growth. It could do so by giving people more confidence in financial intermediaries on average through time.
It could be that putting the symbol "FDIC insured" on the door of banks is a very inexpensive signaling mechanism with a lot of social benefits. It could be argued that without that signaling mechanism, financial intermediation would be much more costly than it is today.
I am not saying that this is definitely true. However, I do think that it is the key issue in banking theory. It is all about the costs and benefits, including moral hazard and regulatory costs, of different signaling mechanisms.