Niall Ferguson outlines the tragedy well but stumbles at the last fence:

As popularised by the ecologist Garrett Hardin, the
tragedy is that an area of open pasture will tend to be depleted and
eventually destroyed if the benefits of exploitation accrue to
individuals, while the costs of exploitation (what economists like to
call the "negative externalities") are shared.

When
people dump rubbish in the sea they are acting like a medieval farmer
who over-grazed the common land. The rubbish is disposed of at no cost
to the polluter, just as the farmer’s cattle got fed for free. But
everyone loses if the sea becomes a cesspit, just as everyone lost if
the commons became a desert.

There are two classic
solutions to this kind of problem. The first is regulation by a higher
authority. In the case of the oceans, this solution is already in
place, in the form of the 1994 United Nations Convention on the Law of
the Sea. The problem, as with so many UN documents, is the lack of
effective enforcement.

So what about the
alternative solution, namely privatisation? In early-modern England,
common land was progressively "enclosed": claimed and fenced by
individual landowners.

In theory, of course, some
parts of the sea have already been enclosed, in that countries with
coastlines lay claim to coastal waters and fisheries. British coastal
waters extend for 12 nautical miles from shore; the exclusive fishing
zone we claim is 200 nautical miles wide.

Yet even if all such claims were universally respected, vast tracts of the world’s oceans would remain "no man’s water".

In
any case, it is far from clear that national governments are effective
custodians even of their own coastal waters, since it is precisely
there that most pollution of the sea occurs. Moreover, it is national
governments that effectively subsidise over-fishing.

What he describes as the two alternatives are in fact both the "regulation by a higher authority". The way that national governments (and while much of the ocean is indeed still a commons, all the major fishing grounds, bar one, are inside those 200 mile limits) dole out the licences and quotas to fish mean that the incentives faced by the fishermen are still the same. Take what you can get now.

There is a role for governments here, which is in the creation of property rights. These should then be owned by the fishermen themselves: that would be true privatisation and the only logical solution to the current problems.