I need to find a simple game in which several people need to interact with each other. The game should be simple for an analysis (it should be simple to describe what happens in the game, what players did). Because of the last reason, the video games are not appropriate for my purposes. I am thinking of a simple, schematic, strategic game where people can make a limited set of simple moves.

Moreover, the moves of the game should be conditioned not only by a pure logic (like in chess or go). The behavior in the game should depend on psychological factors, on relations between people. In more details, I think it should be a cooperation game where people make their decisions based on mutual trust. It would be nice if players can express punishment and forgiveness in the game.

Does anybody knows a game that is close to what I have described above?

ADDED

I need to add that I need a game where actions of players are simple and easy to formalize. Because of that I cannot use verbal games (where communication between players is important). By simple actions I understand, for example, moves on the board from one position to another one, or passing chips from one player to another one and so on.