The Prisoner's Dilemma is a well-studied game in game theory, where supposedly rational incentive following leads to both players stabbing each other in the back and being worse off than if they had cooperated.
The original formulation, via Wikipedia:
Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The possible outcomes are: