4 years ago

Duality between cooperation and defection in the presence of tit-for-tat in replicator dynamics

The prisoner’s dilemma describes a conflict between a pair of players, in which defection is a dominant strategy whereas cooperation is collectively optimal. The iterated version of the dilemma has been extensively studied to understand the emergence of cooperation. In the evolutionary context, the iterated prisoner’s dilemma is often combined with population dynamics, in which a more successful strategy replicates itself with a higher growth rate. Here, we investigate the replicator dynamics of three representative strategies, i.e., unconditional cooperation, unconditional defection, and tit-for-tat, which prescribes reciprocal cooperation by mimicking the opponent’s previous move. Our finding is that the dynamics is self-dual in the sense that it remains invariant when we apply time reversal and exchange the fractions of unconditional cooperators and defectors in the population. The duality implies that the fractions can be equalized by tit-for-tat players, although unconditional cooperation is still dominated by defection. Furthermore, we find that mutation among the strategies breaks the exact duality in such a way that cooperation is more favored than defection, as long as the cost-to-benefit ratio of cooperation is small.

Publisher URL: www.sciencedirect.com/science

DOI: S0022519317303570

You might also like
Discover & Discuss Important Research

Keeping up-to-date with research can feel impossible, with papers being published faster than you'll ever be able to read them. That's where Researcher comes in: we're simplifying discovery and making important discussions happen. With over 19,000 sources, including peer-reviewed journals, preprints, blogs, universities, podcasts and Live events across 10 research areas, you'll never miss what's important to you. It's like social media, but better. Oh, and we should mention - it's free.

  • Download from Google Play
  • Download from App Store
  • Download from AppInChina

Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.