Invincible Strategies of Iterated Prisoner's Dilemma

The Iterated Prisoner's Dilemma (IPD) is a well-known benchmark for studying rational agents' long term behaviour such as how cooperation can emerge among selfish and unrelated agents that need to co-exist over long term. Many well-known strategies have been studied, from the simple tit-for-tat (TFT) made famous by Axelrod after his influential tournaments 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 discuss its relationship with some other classes of strategies.