That problem is similar to the problems that existed before the US government monopolized money printing. Banks use to print their own bank notes and it was up to each merchant to decide if he would accept this note or that. The problem was solved by the banks themselves. They began printing and issuing lists of banknotes and discount values based on the bank's confidence that it could redeem the notes for gold. If a bank wanted it's notes to be accepted it had to establish a good track record in the eyes of the other banks. There is no reason to think it will be any different with electronic money.
There is no reason to think it will be any different with electronic money.
It would be very different with electronic money.
A better analogy would be a computer virus. A hacker writes a computer virus and deposits it on one computer, infecting it. The virus seeks out 10 other computers connected to the original computer and replicates itself onto them. Those 10 copies replicate themselves onto 10 other computers. And so on, and so on, until millions of computers are infected with the virus. It only stops when someone identifies the virus, and creates a program to clean the virus off computers. Of course, that only happens if millions of computer owners run the program, and if the virus has some unique identifer that indicates it is the virus (usually a unique series of number embeded in the code).
Think of that same scenario, only with people spending money. Originally created as a false database entry, the money is spent and respent until millions of accounts contain the false dollars. The problem is that, unlike computer code that is a static series of 1’s and 0’s (so you can detect a pattern in the file that indicates this is the virus file) there is no way to identify the false dollars are false. They are just entries in a database. The only way to fix the problem is undo millions of transactions.