What if, in our fictional economy there are two bankers?
There are quite a few options -
1) Expose the other banker
This one is pretty simple - there are many ways to expose a fraudster, not just by releasing money as debt videos. It has the danger of possibly exposing both bankers and threatening the idea of banking in general but that can be handled by (for example) buying the other bank, stepping in to guarantee peoples savings in a run and so forth.
2) Borrow from the other banker and relend at a higher interest rate/higher fee or lower interest rate/lower fee
The higher interest rate one is easy to understand, I assume - one banker piggy backs onto the other and makes some money on the differential. High street banks borrow from the central bank and then make use of this differential, for example. Equally, one could borrow a large amount of money and lend it out at a lower interest rate than a competitor in the hope of capturing more market share.
3) Collaborate with the other banker
A wide variety of ways to do this - the sharing of credit scoring, pooled funds to lend, information sharing, providing apparently independent expert witnesses for trials, agreements on reserve ratios, interest rates etc. All cartels have the problem of uneven rewards though.
4) Store items with the other banker when they can't be loaned out
Storing anything valuable carries risk. Risk of damage/theft/natural disaster. Much better, therefore, to push that cost onto someone else (especially if you are being paid for it and there is a differential.)
5) Buy out the other banker
6) Sell up to the other banker
Also straightforward. In both examples of selling up and buying, accurate pricing would be a problem, as would stopping the other banker starting up a brand new bank. Confidence tricks require confidence and if something is to be bought or sold, one can assume confidence is there enough to start up a new bank.
7) Remove the other banker by some other method - kill him, ruin his reputation, have him imprisoned etc
Easy to see if one checks the history of banking. Wars, assassinations of both body and character, bought regulators, bought judges and so forth are all part of the history of banking. Mind you, people have fought turf wars over ice cream distribution as well, so it's not an exclusive banker hobby.
8) Agree spheres of influence - geographical, business type or whatever
Banker A does commercial banking, banker B does retail. This makes sense from a specialisation standpoint. We can also see this with our currency - the area of banker influence where pounds dominate is called the United Kingdom, the euro has different banking masters, the dollar still others.
9) Secretly merge with the other banker but feign competition
Every apparently competitive high street bank is just a branch of the Central Bank. They are franchises, not seperate businesses. This provides an illusion of competition, the illusion of choice and also allows for insane money growth and massive economic control. This system also eliminates risks.
The largest problem with having two banks is one of expansion and collapse because no one really knows where anything is, who it really belongs to or how to sort out the mess once it's begun.
John deposits £100 at bank A. Bank A lends it to Dave who spends it at Stans shop.
Stan deposits it in bank B. Bank B lends it to Sarah, who doesn't need it right now and so deposits it with her bank, Bank A.
What a tangled mess! And we know who traded with who and when and where. This global perspective isn't available in the real world and it becomes a matter of who can prove what in court. Bankers keep records, other people don't.
There are now lots of accounts, which are partial recording of events - specifically who owes the bank and who each bank owes to. This limited perspective is where the bankers can get their greatest power from - the ability to claim assets whilst holding the cash they claim to be owed.
So, we have £100 now, which is in Bank A, and several people all under the impression that it is theirs. It's still Johns money. the only way to sort the tangled web out (which no individual within the system has any definite idea of although the bankers have a general idea of what is going on) is for each transaction to accurately reverse.
The chances of the unravelling happening in the right order are nil. therefore all banking systems must expand to the point at which they cannot go any farther and will then collapse very messily indeed. There is no need fo this to happen, however - by rights all debts from both sides should be cancelled because they never happened and the owner should claim their property back.
This means all paper currency being returned to the source, which is the central bank and all debts being cancelled.
Next - What happens if people agree that the bank can loan their money out.
So far we have assumed that depositors are in ignorance and of course this is not always the case.