I look at the history to help determine the syntax of the story (see "I understand the story") to give an idea about the amount of emotion involved and the ways people are evolving the dispute.
So, for example, making the first co-operative move when there is a history of confrontation may be difficult, as it may be falsely mistaken as a sign of weakness by others, On the other hand if this is not done, confrontations may often escalate out of all proportion to the intial dispute, creating the intense emotions necessary to justify the sacrifices made.
Constructing a history is also useful for clients as it shows the way confrontation management works. Forecasting a result becomes easier as the clients will by then be familiar with the language of the card table and changes to it..
The history of the story also will bring out two emotions, revenge and gratitude. If in the past, another party has done wrong, then there will be a desire for revenge. if it has done good then there will be a desire to show gratutude. The strength of these emotions and the way in which they affect the way a party behaves depends strongly on the individuals, the culture they are from and the nature of the actions taken.