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 this last reason, 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 not be conditioned 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 detail, 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
As requested, I would like to provide more details. I do want to use a game for experimental purposes. To elaborate, my hypothesis is that people play differently depending on who their partner is in the game. Or, in other words, a player's strategies depend on their interpersonal relations. It is a very general statement. At the moment I do not know what kind of interpersonal relations can exist. In the simplest case we can speak about "friends" and "strangers" (people who know or do not know each other). Another aspect of interpersonal relations I can think of is trust. People can play differently depending on the level of trust between them.
I am looking for a game that captures several aspects of interpersonal relations. The repeated Prisoner Dilemma game is close to what I need. But I am afraid that it is too trivial (people will just cooperate).