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 strateg...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2024-02
Main Authors: Glynatsi, Nikoleta E, Nowak, Martin A, Hilbe, Christian
Format: Article
Language:English
Subjects:
Algorithms
Cooperation
Strategy
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422