Therefore, I think that a more effective and efficient incentive should be based on both 1 and 2.
Using the cobra example again, the government can setup the following:
1. If the number of cobras reduces to amount X after 1 year, there will be an reward pool Y.
2. The less number of cobras(as long as it's below X), the larger the reward pool Y.
3. The amount of the reward pool Y is capped at Z.
4. The minimum share for those actively acting on the cobra issue is W.
5. The more one actively acting on the cobra issue, the larger share, which is capped at T, one can take, as long as 4 still holds.
6. Cobra skins coming from cobras bred by someone will be rejected by the government and the offenders will be blacklisted
Obviously, this setup won't lead to those actively acting on the cobra issue feeling unfair due to those not acting on it at all taking the exact same amount of rewards as them, as long as the value of W is properly set(They might still feel cheated by those breeding cobras, which will be explain below).
Now, the only reason for anyone to breed cobras will be to take a larger share of the reward pool Y, which is still based on the number of cobras reduced after 1 year.
It means that breeding too many cobras can actually make those breeding cobras lose, as doing so still have costs and can lead to the decreased amount of the reward pool Y.
This implies both the risk of cheating money from the government and the number of cobras being increased will become far smaller, more controllable and manageable.
At the very least, even if someone still breeds cobra in order to take a larger share, he/she still won't go overboard, meaning that the government won't have to abandon the setup completely. Instead, just blacklisting him/her and using the media against him/her can suffice.
Also, this setup can detect the seriousness of frauds very easily, just by comparing the number of cobras reduced after 1 year and that of the cobra skins received by the government during the year.
Finally, this setup is much more configurable albeit also much more complicated, as there are much more parameters to be tweaked in order for the setup to work properly.
Of course, this setup is still not really that ideal and is still quite vulnerable to this slightly extreme case:
1. Most people being able to breed cobras will think that many others will really reduce the number of cobras by a rather huge amount
2. They can just breed cobras and can still be able to take a large share of the reward pool Y without being caught by the government
3. The majority of those actively reducing the number of cobras feel cheated due to them taking less rewards than those breeding cobras
4. The aforementioned majority gives up on continuing to reduce the number of cobras
5. The entire setup fails due to not meeting its goal to have a reward pool Y
6. Those breeding cobras releases all the cobras they've bred, causing the number of cobras to be increased
Nevertheless, I still think that it'll work better than the original setup and the aforementioned case's much more extreme than the original one.
Another issue of this setup is that it has a somewhat limited application.
For instance, it won't work well on police fighting crimes.
It's because only police can know the true number of crimes, meaning that this setup would incentivize them to report a false crime number that's far lower than the true one, as it costs far less than actively changing the environments from breeding crimes.
But since reporting a false number alone won't work without them being less active on hunting crimes which will also reduce their costs(otherwise the liar would be too obvious), they would also be incentivized to hide those actual crimes from the public(which still costs less than addressing the root causes), or the sheer high number of incidences induced by crimes would discredit them.
This leads to many criminals thinking that they can commit more crimes with less chances being caught, which lead to the increased number of crimes.
So this setup won't work properly if the only entities knowing the true results of a setup are those taking rewards from that setup.