Conditional cooperation with longer memory
<|reference_start|>Conditional cooperation with longer memory: Direct reciprocity is a wide-spread mechanism for evolution of cooperation. In repeated interactions, players can condition their behavior on previous outcomes. A well known approach is given by reactive strategies, which respond to the co-player's previous move. Here we extend reactive strategies to longer memories. A reactive-$n$ strategy takes into account the sequence of the last $n$ moves of the co-player. A reactive-$n$ counting strategy records how often the co-player has cooperated during the last $n$ rounds. We derive an algorithm to identify all partner strategies among reactive-$n$ strategies. We give explicit conditions for all partner strategies among reactive-2, reactive-3 strategies, and reactive-$n$ counting strategies. Partner strategies are those that ensure mutual cooperation without exploitation. We perform evolutionary simulations and find that longer memory increases the average cooperation rate for reactive-$n$ strategies but not for reactive counting strategies. Paying attention to the sequence of moves is necessary for reaping the advantages of longer memory.<|reference_end|>
@article{glynatsi2024conditional,
    title={Conditional cooperation with longer memory},
    author={Nikoleta E. Glynatsi, Martin A. Nowak, Christian Hilbe},
    journal={arXiv preprint arXiv:2402.02437},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.02437},
    primaryClass={cs.GT physics.soc-ph}
}