The other side is also not necessarily irrational, but much less deterministic. For example, there is the question if the board even wants to sell, if they like the potential buyer, if they have a vision for the company that aligns with the buyer and some non-tangibles. Charisma projection and speech-craft definitely has an influence too, as has track record.
The more factors are in alignment with the board, the closer the price is to the stock value. The more hostile the negotiation, the more it moves away.