It could if the reward wasn't reduced fast enough. At some point, the reward should go to zero. And everyone should know in advance that it's going to go to zero at some point.
It would be difficult to find the right reduction function. If the reduction is too slow, the snake-breeders become a problem. If the reduction is too fast, there is no effect at all.
Wouldn't this result in locals just breeding more and more and more cobras to cope with the decreasing reward?