A study on emergence of alternating reciprocity in a 2 × 2 game with 2-length memory strategy

It is recognized that bilateral cooperation (C), a reward-state in other words, emergently comes up in a 2 × 2 prisoner's dilemma game, if you assume a strategy set with a memory concept. Also observed is a mixture state of cooperation (C) and defect (D), saint- and temptation-state in other words, to obtain a higher payoff than R (R reciprocity) in a hero or leader game that is a chicken-type dilemma game; this phenomenon is called alternating reciprocity (AR) or ST reciprocity. Observing a holistic 2 × 2 game world including trivial games and various dilemma games, where 2-length memory and infinite interactions are assumed, the paper reports on the specific mechanism of AR. It is observed there are three different phases relating to AR, which can be explained by the stress of the dilemma.