Jason predicts that in the battle between Elon Musk and the Twitter board, initially there will be resistance from the board which might lead to a stock collapse. Despite the initial skepticism, Elon will persist and lower his offer, eventually winning the deal by the end of the year with a reduced bid. The ongoing negotiation strategy involves gradual reduction in the offer price until the board agrees, with Jason drawing a parallel to a strategic approach reminiscent of the character Michael Corleone from 'The Godfather'.