It is worth making the distinction between "teambuilding" as an activity and "team building" as a process.
Teambuilding activities typically involve a retreat of some sort (an activity outside the formal work environment), typically organized with help from external consultants, with a series of communication, trust, and mutual understanding activities that can let people experience effective teamwork in a low risk environment. "Team building" as a process is the long term building of the team, from disparate individuals into a high performing team.
In regards to negotiations within a team one can look at the ‘Game Theory’ as a competitive game which can be summarized by its underlying theory "the prisoner's dilemma".
Here's a quick 2 min video on what this is if you've never heard of it: