A bibliometric study of research topics, collaboration, and centrality in the iterated prisoner's dilemma

The Prisoner’s Dilemma (PD) has been used since the 1950s as a framework for studying the emergence of cooperation across mathematical, social, biological, and ecological sciences. This manuscript presents a bibliometric analysis of 2420+ published articles on the PD between 1951 and 2018 to examine what topics are researched, how these topics have changed over time, and how collaborative the field is. Using Latent Dirichlet Allocation (LDA), the paper identifies research topics within PD publications and examines their temporal dynamics. The study also analyzes authors’ collaborative behavior via the co-authorship network, and combines topic modeling with network analysis to assess which authors are most central overall and within topics. The overarching aim is to assess collaborative behavior in a field whose core focus is cooperation itself, situating the work within broader bibliometric approaches that have been used to understand field development, collaboration, and productivity.

Prior scholarship has used bibliometrics to support historical accounts of field development, link scientific growth to policy, understand author order, and investigate collaborative structures in interdisciplinary domains. Co-authorship network analysis has become a key method for quantifying collaboration (e.g., average degree, clustering coefficient, community structure) and has been applied to fields such as the evolution of cooperation and cultural evolution. LDA topic modeling (Blei et al., 2003) has been broadly applied to scholarly corpora to uncover topic structures and temporal trends, including in mathematics education, information science dissertations, and EvoLang conference content. Bergmann and Dale (2018) combined LDA with clustering and co-authorship analysis. Building on these works (Bergmann and Dale, 2018; Liu and Xia, 2015; Youngblood and Lahti, 2018), the present study extends methodology by integrating LDA-derived topics with co-authorship network analysis and applies it to a new, multi-source PD dataset.

Data were collected programmatically via publisher APIs using a custom Python library (Glynatsi, 2017) from five sources: arXiv, PLOS, IEEE Xplore, Nature, and Springer. Search terms included variations of “prisoner’s dilemma” and related phrases (e.g., “prisoners evolution”, “prisoner game theory”) applied to title, abstract, or full text fields. After retrieval (latest on 11/30/2018), a cleaning process removed duplicates (e.g., preprints vs. published versions) via semantic title matching, standardized author names (e.g., collapsing “Martin Nowak” and “Martin A. Nowak”), and excluded non-relevant items identified by text-term matches. An additional 76 historically important PD-related articles not in the sources were manually added (e.g., Flood, 1958; Ohtsuki et al., 2006; Stewart and Plotkin, 2012; Axelrod’s seminal works). The resulting dataset contains 2422 unique- title articles (with a broader provenance summary indicating substantial contributions from arXiv, Springer, PLOS, IEEE, and Nature). Time-series analysis (1951–2018) showed a steady increase since the 1980s with an exponential model forecasting continued growth; a dip in 2017–2018 was attributed to incomplete API coverage. Collaboration statistics showed 4226 unique authors, a Collaboration Index (average authors on multi-authored papers) of 3.2, and 22% single-author papers (545 in total). LDA topic modeling (gensim) was applied to abstracts to identify latent topics; models with different topic counts were compared using coherence and exclusivity (with custom code archived). Based on coherence (near-max) and better exclusivity, n=5 topics were selected for primary analysis, with additional cumulative-period models (varying n based on coherence) for temporal validation. Co-authorship networks were built using NetworkX: nodes are authors; edges connect co-authors. Graph metrics computed include number of components, size of largest component, average degree, clustering coefficient, number of communities (Clauset-Newman-Moore), and modularity (Louvain). Centrality was assessed via closeness and betweenness. Comparative datasets for “Auction games” and “Price of Anarchy” were also collected and analyzed similarly for benchmarking.

• Topic modeling identified five coherent PD research topics: (A) human subject research; (B) biological studies; (C) strategies; (D) evolutionary dynamics on networks; (E) modeling problems as a PD game (non-biological applications). Each topic has persisted over time with no decreasing trend; publication counts rise after topic introduction and remain active.
• Model selection: Coherence was highest for n=6 and near-high for n=5; exclusivity favored n=5, which was used. Over cumulative periods, an n=6 model often fit slightly better, but differences were small, and the five-topic model’s relevance increased over time.
• Dataset/time series: Publications increased steadily since the 1980s (Axelrod’s computer tournaments era); an exponential fit forecasts continued growth despite an apparent 2017–2018 dip due to data incompleteness.
• Authorship: 4226 authors; Collaboration Index 3.2; 22% single-author papers (545). Matjaž Perc had the most publications (83).
• Co-authorship network (full PD): |V|≈4221–4226 authors; |E|=7642; 1157 connected components; largest component size 796. Average degree ≈3.6; clustering coefficient ≈0.666; high modularity ≈0.965 with many communities, indicating strong within-community collaboration and sparse cross-community ties.
• Main cluster (largest component): average degree ≈5.6; clustering coefficient ≈0.773; modularity ≈0.840; 29 communities in the main cluster.
• Comparison with other game-theoretic fields: PD is more collaborative than “Auction games” (avg degree 2.93; clustering 0.599; 8.4% isolated nodes) and “Price of Anarchy” (avg degree 2.97; clustering 0.626; 12.5% isolated nodes), and has fewer isolated authors (≈8.0%).
• Topic-specific networks: Topics A (human studies) and B (biological studies) show higher average degrees and clustering, with fewer isolated nodes; Topic C (strategies) has the lowest average degree; Topic E (modeling problems) has the highest proportion of isolated authors. Topic D (evolutionary dynamics on networks) is notably collaborative and forms a subgraph of the main cluster.
• Centrality: Most central authors (betweenness and closeness) are those connected to the main cluster; Matjaž Perc is most central in both measures. Other highly central authors include Zhen Wang, Long Wang, Yamir Moreno, Attila Szolnoki, Martin Nowak, and others. Topic-level centralities are generally low except Topic D, whose central authors overlap with the main cluster.

The study’s core question—how PD research topics have evolved and how collaborative the field is—was addressed by integrating LDA topic modeling with co-authorship network analysis. The five discovered topics capture the interdisciplinary breadth of PD research and show stable, ongoing activity without evidence of topic obsolescence. The co-authorship analysis reveals PD as comparatively collaborative among game-theoretic fields, with moderately high average degree and clustering and relatively few isolated authors. However, high modularity and many communities indicate collaboration tends to occur within rather than across groups, limiting cross-community connectivity. Centrality analyses show that perceived influence is concentrated in the main cluster and closely associated with work on evolutionary dynamics on networks (Topic D), suggesting that this topic acts as a hub that connects many researchers and collaborations. This pattern helps explain how collaboration structure correlates with author centrality and influence in PD research.

This work identified five enduring PD research topics—human subject research, biological studies, strategies, evolutionary dynamics on networks, and modeling problems as a PD—and showed that the PD field continues to attract attention and grow. Co-authorship analysis demonstrated that PD research is relatively collaborative compared to other game-theoretic domains, yet characterized by high modularity and communities with limited cross-group ties. Central authors are predominantly those embedded in the main cluster, largely publishing in evolutionary dynamics on networks, indicating greater collaboration and influence in that topic. Future work could extend the approach to additional game-theoretic subfields and incorporate edge weights to capture tie strength; preliminary checks suggest weighted analyses would not alter the main conclusions. The code and data have been archived to enable reproducibility and reuse.

• Coverage is constrained by selected sources (five APIs) and specific search terms; relevant papers using alternative terminology (e.g., “donation game”) may be underrepresented. The authors note that results generalize to stated goals but are inferred from the chosen terms and fields.
• API-based retrieval can be incomplete or delayed, particularly for recent years (2017–2018), affecting time-series counts.
• Manual curation added 76 key articles; while improving coverage, it introduces a degree of selection bias.
• Author name disambiguation was addressed via semantic similarity and manual checks, but residual ambiguities may remain.
• Network analyses used unweighted co-authorship edges; multiple collaborations between pairs were not encoded as tie strength (though preliminary checks suggested main results are robust).
• Topic modeling relies on abstracts and a fixed number of topics; model selection (n=5) balanced coherence and exclusivity, but alternative choices (e.g., n=6) fit some periods slightly better.