PC Interactions

Group Dynamics in the Game
A role-playing or adventure game has an implied social contract. Really any game can. It is implied that everyone wishes to have fun together, that everyone will be respected and that each will have a part to play. Furthermore, it is implied that rules will fairly apply to everyone and that any disputes will be handled in a fair and friendly manner. Do games occasionally fall short of these expectations, of course they do. But I believe a usually unstated assumption of something similar to this social contract is a cornerstone of the hobby.
Hobby folks, as a group are welcoming and eager to share their interest with anyone who shows a similar interest in the hobby. The role-playing hobby from the start has been about showing others how to play the game and sharing in a fun experience. White Box and other game rule systems are set up with a subtle, but powerful group dynamic mechanic to ensure that group fun happens. The class system creates distinct player characters with a niche to fill during the game. No one PC has all the necessary skills and abilities for success and must depend on other PCs in some situations, other PCs have other specialties because they are of another class. This is a unifying mechanic. The game is set-up to be cooperative.
Conflicts are interesting and factions are also a part of the game. White Box allows for PCs to be one of four races roughly based off the fiction of J.R.R. Tolkien (although Mr. Gygax would minimize this connection), humans, elves, dwarves and hobbits (later changed to halflings after the Tolkien Estate contacted TSR). Friction between elves and dwarves is the stuff of legend and frequently enters the game as good-natured banter.
The PC is assigned an alignment by the player, either Law, Chaos or Neutrality in the White Box. This is an idea drawn from literature (Poul Anderson and Michael Moorcock) and intended to be an artificial division of all creatures in the fantastic setting into "teams" or "forces" which oppose one another. The forces of Chaos naturally work against the forces of Law. Neutrality seems to be folks just out for themselves. Game conflict is inevitable and forms the basis of a good guys/bad guys paradigm. 
In reaction to the question, "What does my PC do when not adventuring?" game designers put forth rules for how the PC fits into the fictional society. Games including Chivalry & Sorcery and RuneQuest emphasize the PC's role in the fantasy society. In these games players are encouraged to role-play their PCs interacting with other PC and NPC members of  the shared fiction, forming relationships and progressing upward in society thereby playing a larger role in the setting. Role-playing the same sorts of situations which may occur in real life, such as asking a stranger in a position of power for assistance or confronting a person abusing their power, or just finding out what they know about a missing person is often the goal of a session of play.
From its earliest days the game, regardless of rules used, has been set up as a social interaction using a shared fiction with fun and excitement for all as the goal. Ultimately something more than that usually happens. Social skills are practiced, friendships are formed and stories are made. Stories which then become part of our shared history.