Quoting XDCD:
Since games don't have 'real' consequenses it'll be too easy to manipulate debt, thus a real-world scenario sadly wouldn't work.
One thing that the stock market simulation HSX did long ago (this was probably discontinued) was pegging their HSX $ to a currency, in their case, American dollars. It was probably some small fraction of a penny, but then they created a store where people could buy things with their HSX $, e.g., t-shirts and so forth.