Reciprocity phase in various 2×2 games by agents equipped with two-memory length strategy encouraged by grouping for interaction and adaptation

This paper numerically investigates 2×2 games involving the Prisoner's Dilemma, Chicken, Hero, Leader, Stag Hunt, and Trivial Games in which agents have a strategy expressed by five-bit, two-memory length. Our motivation is to explore how grouping for game interaction and strategy adaptation influence ST reciprocity and R reciprocity (Tanimoto and Sagara, 2007a [Tanimoto, J., Sagara, H., 2007a. A study on emergence of coordinated alternating reciprocity in a 2×2 game with 2-memory length strategy. Biosystems 90(3), 728-737]. Enhanced R reciprocity is observed with the stronger grouping for game interaction when a relatively stronger grouping for strategy adaptation is assumed. On the other hand, enhanced ST reciprocity emerged with the stronger grouping for strategy adaptation when the relatively weaker grouping for game interaction is imposed. Our numerical experiment deals with those two groupings independently and dependently.