Nice Invincible Strategy for the Average-Payoff IPD

The Iterated Prisoner's Dilemma (IPD) is a well-known benchmark for studying the long term behaviours of rational agents. Many well-known strategies have been studied, from the simple tit-for-tat (TFT) to more involved ones like zero determinant and extortionate strategies studied recently by Press and Dyson. In this paper, we consider what we call invincible strategies. These are ones that will never lose against any other strategy in terms of average payoff in the limit. We provide a simple characterization of this class of strategies, and show that invincible strategies can also be nice. We discuss its relationship with some important strategies and generalize our results to some typical repeated 2x2 games. It's known that experimentally, nice strategies like the TFT and extortionate ones can act as catalysts for the evolution of cooperation. Our experiments show that this is also the case for some invincible strategies that are neither nice nor extortionate.