hah, the problem is, and now I'm getting into neoclassical economics, at scale farming is easier than foraging. As in, the cost of rat reproduction < cost of (rat discovery + capture + disease risk) so there's no place to set a bounty since it's always more efficient and reliable to produce rats than to competitively find them.

Incentive programs works for say cans, because the cost of pulling them out of the waste stream is less then the cost of building a factory to produce them. But for hearty robust animals that eat garbage and have lots of offspring, probably not.

As far as a working system, we should look to Alberta (https://alberta.ca/albertas-rat-control-program.aspx) - lots of free resources and budget is set aside for rat proofing and removal - as in calling in exterminators and DIY rat killing things (such as poison) are free.

Call that socialism if you want, it's worked for decades.