How do exchanges keep relatively similar price on coins? I know there are price difference across all exchanges but they are relatively similar.  If each exchange operated independently I would think the price of coins would be radically different since the liquidity and exchange pattern would have nothing to do with each other.  Are exchanges tied to a central index?  How do they keep a somewhat "consistent" price?
If I could buy a bitcoin on Exchange A for $2,000, turn around and immediately sell it on Exchange B for $2,500, and make an immediate profit of $500, I would do that all day long, and get rich!

But if even a small price discrepancy exists between two exchanges, many people will find it, and start buying on one/selling on the other. 

All that one-sided buying in one market and selling in the other market moves the price back to equilibrium.