Yes, the stock market is automated-- and highly regulated.
Of course, the stock market is limited to publicly traded stocks, and there are all kinds of regulations applying to the actions of the companies traded.
If you are really interested in this area, you might want to start here:
What if I just add a place for visitors to donate and in return for donations I offer an arbitrarily small percentage of the company that just so happens to be proportional to the donation amount? Those who donate will just have to take my word for it. :P