My favourite illustration of this is in The Wire. The city wants to crack down on crime and increases the target number of arrests. The police chief sends out the word and police officers begin making a bunch of spurious arrests. Do you blame the politicians for picking crappy metrics and for their poor understanding of human nature? Or do you blame the individuals who choose to exploit the metric out of self-interest? Plenty of blame to go around.
The textbook example is when they wanted to reduce the rat population somewhere and paid people for (catching and) bringing in dead rats. Instead, people started to breed them and "sell" the dead specimens to the city.