I really don't think it's going to come down to one team winning by outbidding the other by $5 mill.
When the Yankees signed Cole, there were reportedly 3 teams who offered him 8 years @ $36. The Yankees won by making it 9 years @ $36.
When the Cubs outbid the Sox for Lester, the teams had both reportedly offered $135 mill, and Theo won by jumping the bid to $155 mill.
It's like you really have to establish that you are the one who will not be outbid by doing something extra crazy.