I am fairly certain the cobra story is incorrect as traditionally given. I haven't found any historians who have commented on it since the 1960s (which is itself suspicious) so I found primary sources as close to the event as I could and did some interpolation over the different accounts. (One recent scholarly book, admittedly not in a historical area, just cites the Freaknomics podcast website. Facepalm.)

The bounty regarding dangerous snakes (not just cobras) started roughly around 1875 and the bounty underwent a change (not removal) around 1895, so I put together several accounts from that time. The goal was to drop the number of deaths (both from people and animals) but it remained steady each year around 19,000.

Year | Death Rate

1891 | 21389

1892 | 19025

1893 | 21213

Noteworthy here is that 84,789 reptiles were paid for in 1892 and 117,120 were paid for in 1893. It was suspected and not proven that people were raising snakes for the bounty. Someone who is loose with the facts might also try to conclude that the cobras were simply freed at this point which caused the error (this is definitely not the case as the bounty hadn't changed yet.) A more sober analysis has the bouncing figure of deaths was consistently around statistical error and my sources suggested it constantly hovered near the same number with a floor of 19,000 -- so, there was no "bounce" caused by the raising, just no appreciable drop. Simultaneous with the snake bounty was a bounty on wild animals like tigers, and nobody is suggesting that it caused a raising of tigers, yet there was similarly no dent made in the number of deaths.

The bounty was reduced shortly after, and again, no particular change in the deaths by snake. It essentially became not worth it enough to find eggs and raise snakes; however, any snakes that were still in easy possession were still worth money. So they likely were not simply let free, as the story goes. (And in terms of statistical evidence, no source gives evidence of rise in snake count.) People simply went back to slaying snakes when they saw them.

However, the whole bounty system did led to greater awareness of the habits of snakes, and two reforms were introduced: removing underbrush from nearby villages, and getting farmers to wear thicker boots.

The result?

Death of farmers was reduced: the boots were successful. Deaths in Bombay, Burma, and Hyderabad -- generally from fields -- were reduced.

Death in houses was increased: unfortunately, the destruction of underbrush meant more snakes decided to go indoors. Rats and frogs (which they hunted) in particular were more likely to go into houses, and the snakes followed.

So rather than the tidy morality story of economics, we have a bit more of a muddle. The snake bounty didn't cause an overall increase of population in the wild, as the bounty wasn't made zero -- it just didn't become profitable to go through the trouble of raising snakes any more. (I don't know what year the bounty was fully phased out, but the professionals seem to have stopped when there was still a bounty.) The whole effort led to some practical realizations about footwear which actually helped save lives, but attempting to act on one of the other pieces of information -- about the underbrush -- really did cause an adverse effect.

...

Primary sources used:

Chambers's Journal. (1895). United Kingdom: W. & R. Chambers.

Godey's Magazine: Volume 136. (1897). United States: Godey Company.

Yearbook of the United States Department of Agriculture. (1897). Washington Government Printing Office.

Apologies-- is the question whether or not the story of the British Raj is true, or are you just asking for examples of other perverse incentives?

The example from Hanoi definitely occurred, and historian Michael Vann has written about it and even published a graphic novelization through Oxford Press on the episode. I use that book in the classroom and find it incredibly useful to highlight and illustrate colonial views on urbanization, health, the civilizing mission, and empire. Vann's analysis centers on Hanoi during the Third Plague Pandemic, an outbreak of bubonic plague across colonial ports from 1890 to 1905 with subsequent aftershocks over the next couple of decades.

French officials in Hanoi offered a bounty on rats to combat the spread of bubonic plague in the city. Somewhat ironically rats were a problem as their population had grown in the new urban underworld the French had created— the sewers of the French/white quarter of the city. The rat bounty led some enterprising individuals to begin breeding rats that they could turn into the French to collect the bounty. This was far safer and easier than hunting them in the sewers. However, when the bounty was reduced and eventually eliminated, many of the rats may have been released.

Vann tracks the story through colonial reports, especially those detailing the number of bounties paid and debates over the value of the program. He refers to this as the “Great Rat Massacre”— a play on words that refers back to Robert Darton’s famous work “The Great Cat Massacre,” a piece that also explores cultural history in unusual circumstances, in Darnton’s case print workers during the Enlightenment.

• Michael G. Vann, “Building Colonial Whiteness on the Red River: Race, Power, and Urbanism in Paul Doumer’s Hanoi, 1897-1902,” Historical Reflections/ Réflexions Historiques Vol. 33, No. 2 (2007): 277-304.

• Ibid, "Of Rats, Rice, and Race: The Great Hanoi Rat Massacre, an Episode in French Colonial History," French Colonial History Vol. 4 (2003): 191-203.

Other colonial authorities followed a similar strategy, for instance, rat bounties were issued in the Australian port of Syndey and the French colonial port of Nouméa. In Nouméa, officials extended the bounty to any four-legged animal seen as polluting the urban environment, including stray dogs and pigs. To my knowledge, no one ever started breeding rats in either of those circumstances-- though it's possible that, unlike Hanoi, they were either never caught or never increased the scale of their operation in such a way that administrators became suspicious.