In an article on the BBC website, the BBC News website's world affairs correspondent Paul Reynolds asks Could 19th-Century plan stop piracy? At one point in the article Reynolds notes,
And the UN Monitoring Group on Somalia issued a damning report last December in which it castigated ship owners for paying ransom.And there is a logic to the UN group's report. Supply curves slope upwards, the more you pay for something the more you get supplied. As far as pirates are concerned, the more money they can make, the more pirate "firms" will enter the market. So if companies pay large ransoms they could be making the piracy problem worse.
"Exorbitant ransom payments have fuelled the growth of [pirate] groups," it stated.
Clearly companies want their ships and crews back and are willing to pay to get them back. But while paying up will get a given ship back it could also increase the likelihood of more ships being taken in the future. Basically paying a ransom, while rational for a single company, conveys a negative externality on all other ship owners since it increases the chance of other ships being taken in the future.