ArticleNature communications2024
Evolutionary dynamics of any multiplayer game on regular graphs.
Article in Nature communications, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 7 papers.
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Who cites it
7 citing papers in PubMed.
- Public goods games on any population structure.Science advances · 2026Article
- Higher-order interactions shape collective human behaviour.Nature human behaviour · 2025Review
- Strategic competition in informal risk-sharing mechanisms versus collective index insurance.Journal of the Royal Society, Interface · 2025Article
- Drivers of cooperation in social dilemmas on higher-order networks.Journal of the Royal Society, Interface · 2025Article
- Revisiting institutional punishment in the N-person prisoner's dilemma.Theory in biosciences = Theorie in den Biowissenschaften · 2025Article
- Article
- Evolutionary Game Dynamics with Environmental Feedback in a Network with Two Communities.Bulletin of mathematical biology · 2024Article
Corrections and comments
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Authors and funding
3 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
Multiplayer games on graphs are at the heart of theoretical descriptions of key evolutionary processes that govern vital social and natural systems. However, a comprehensive theoretical framework for solving multiplayer games with an arbitrary number of strategies on graphs is still missing. Here, we solve this by drawing an analogy with the Balls-and-Boxes problem, based on which we show that the local configuration of multiplayer games on graphs is equivalent to distributing k identical co-players among n distinct strategies. We use this to derive the replicator equation for any n-strategy multiplayer game under weak selection, which can be solved in polynomial time. As an example, we revisit the second-order free-riding problem, where costly punishment cannot truly resolve social dilemmas in a well-mixed population. Yet, in structured populations, we derive an accurate threshold for the punishment strength, beyond which punishment can either lead to the extinction of defection or transform the system into a rock-paper-scissors-like cycle. The analytical solution also qualitatively agrees with the phase diagrams that were previously obtained for non-marginal selection strengths. Our framework thus allows an exploration of any multi-strategy multiplayer game on regular graphs.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.