Examples of the price of abstraction?
Another beautiful example of the price of abstraction: network coding. It's known that in multicast settings, the max-flow-min-cut relation is not one of equality (the primal and dual don't match). However, the traditional models assume flow that's merely passed on and not "processed" in any way. With network coding, you can beat this limit by cleverly combining flows. This example was a great motivator for the study of network coding in the first place.