On some winning strategies for the Iterated Prisoner's Dilemma or Mr. Nice Guy and the Cosa Nostra

We submitted two kinds of strategies to the iterated prisoner's dilemma (IPD) competitions organized by Graham Kendall, Paul Darwen and Xin Yao in 2004 and 2005. Our strategies performed exceedingly well in both years. One type is an intelligent and optimistic enhanced version of the well known TitForTat strategy which we named OmegaTitForTat. It recognizes common behaviour patterns and detects and recovers from repairable mutual defect deadlock situations, otherwise behaving much like TitForTat. The second type consists of a set of strategies working together as a team. These group strategies have one distinguished individual Godfather strategy that plays OmegaTitForTat against non-members while heavily profiting from the behaviour of the other members of his group, the Hitman. The Hitman willingly let themselves being abused by their Godfather while themselves lowering the scores of all other players as much as possible, thus further maximizing the performance of their Godfather in relation to other participants. The study of collusion in the simplified framework of the iterated prisoner's dilemma allows us to draw parallels to many common aspects of reality both in Nature as well as Human Society, and therefore further extends the scope of the iterated prisoner's dilemma as a metaphor for the study of cooperative behaviour in a new and natural direction. We further provide evidence that it will be unavoidable that such group strategies will dominate all future iterated prisoner's dilemma competitions as they can be stealthy camouflaged as non-group strategies with arbitrary subtlety. Moreover, we show that the general problem of recognizing stealth colluding strategies is undecidable in the theoretical sense.