The correct answer is option 4, which states that the Nobel Prize in Physics for the year 2016 was given to David J. Thouless, F. Duncan M. Haldane, and J. Michael Kosterlitz. This means that all three individuals were awarded the Nobel Prize for their contributions to the field of physics in 2016.
Now let`s dissect the other options:
Option 1 states that the prize was given only to David J. Thouless. This option is incorrect because, as stated above, the prize was awarded to multiple individuals.
Option 2 states that the prize was given only to F. Duncan M. Haldane. This option is also incorrect for the same reason mentioned before.
Option 3 states that the prize was given only to J. Michael Kosterlitz. This option is once again incorrect because the prize was awarded to multiple individuals.
In summary, the correct answer is option 4, which correctly states that the Nobel Prize in Physics for the year 2016 was awarded to David J. Thouless, F. Duncan M. Haldane, and J. Michael Kosterlitz.