Why do Skyteam airlines have different prices for the same RTW ticket?
 

The RTWSKY4 fares from LON, for example, are
GBP 1139.00 from OK,
GBP 1199.oo from KE, and
GBP 1259.00 from KL, just to mention some Skyteam airlines.

Why are there these differences in prices? Wouldn't everyone simply
buy their RTW ticket from OK?
Or does buying the ticket from OK come with some restictions? (Is it necessary , for example, that the first leg of the RTW trip is a OK flight if you buy the ticket from OK?)

Thank you very much in advance for your answers!!!

They have to compete to avoid anti-trust. Same reason that they offer different fares on the same routes for other things.

As far as I know there is no requirement to fly on OK for an OK-issued RTW ticket.