The Prisoner's Dilemma problem is the classic problem for examining how computer's (people even!) participate in relationships in which cooperation is beneficial. (I don't have any original references handy yet - I will find them).
Essentially the game examines the benefits of cooperation within a 2 entity relationship using a simple payoff matrix.
2. The game is played in rounds (round-robin etc). Each round consists of 2 entities playing off against each other in a fixed number of games (say 10 games).
3. Each round an entity may either D(efect) or C(ooperate).
If both entities Cooperate they get 3 points each.
If both entities Defect they get 1 point each.
If one entity Defect's while the other Cooperates it get 5 points;
the Cooperating entity gets zero points.
4. Of course the winning entity is the one with the most points. Overall more points can be accumulated by the entities Cooperating; but selfishness may pay off in some cases.
This page was optained from: http://www.cs.rmit.edu.au:80/~geoff/prisoner.html