Open research questions in Evolutionary Game Theory and Cooperation

What the literature leaves open

• It is imperative to acknowledge several inherent limitations of the present study, alongside promising avenues for subsequent scholarly inquiry. First, this study utilized a cross-sectional design, which only measures variables at a single time point and therefore cannot estab- lish causal or longitudinal associations among negative workplace gossip, work engagement, and turnover intention; future research could adopt longitudinal or experimental designs to validate the causal direction and temporal stability of the proposed model. Second, all data were gathered via self-administered questionnaires, which may give rise to common method bias; while statistical analy- ses confirmed minimal bias, future research could incorporate mul- tisource data (e.g., supervisor ratings, peer evaluations, or organizational records) to mitigate subjective reporting bias. Third, this study only explored the mediating function of work engagement, without exploring potential moderating variables that may buffer or strengthen the relationships under investigation; future studies could incorporate personal factors (e.g., psychological capital, emotional intelligence) or contextual factors (e.g., leadership style, organiza- tional climate, social support) as moderators to develop a more com- prehensive moderated mediation model. Fourth, the study employed convenience sampling, which may constrain the generalizability of the results; future research could adopt probability sampling across diverse regions, public and private kindergartens, and urban–rural settings to strengthen representativeness. Fifth, this study focused solely on perceived negative workplace gossip as a unidimensional construct; future studies could distinguish between different forms, sources, or functions of gossip (e.g., victim vs. observer perspectives, gossip from colleagues vs. supervisors) to yield a more detailed and nuanced comprehension. Finally, this study was carried out with Chinese kindergarten teachers within a collectivist cultural context; cross-cultural comparative research could be performed to examine whether the associations differ across individualist and collectivist cultures or among different care-oriented professions.

  Negative workplace gossip and turnover intention among Chinese kindergarten teachers: the mediating role of work engagement · 2026 · DOI

• Although RPS systems have provided a classic framework for understanding cyclic competition and have been extended to include HOIs, the specific effects of these interactions on biodiversity in increasingly complex systems remain uncertain.

  Nonlinear effects of higher-order interactions on pattern formation and species persistence in cyclic ecosystems · 2026 · DOI

• 1. Scalar simplification. The cooperation coefficient αi and voluntariness parame- ter vi are scalar simplifications of complex psychological constructs. A multidimen- sional treatment would capture more of the underlying complexity. 2. Threshold sensitivity. The attractor analysis depends on the initial cooperation index κ(0) exceeding the threshold x∗. While biological evidence supports high initial κ, the precise value of x∗ depends on payoff parameters that may vary across societies and historical periods. 3. Transition dynamics. The model establishes that the platform architecture is superior at equilibrium but does not address the transition problem: how to move from a Leviathan system to a platform system without passing through a period of instability. 4. Scale considerations. Ostrom’s commons governance principles have been demon- strated primarily at local scales. Whether the platform model scales to populations of millions or billions remains an open question, though digital platform technolo- gies provide at least a partial mechanism. 5. Defense against external Leviathans. A platform state in a world of Leviathans faces the unilateral disarmament problem. Defense mechanisms compatible with platform architecture require further development.

  Cooperation as Attractor: A Multi-Level Formal Refutation of Hobbes's Bellum Omnium Contra Omnes · 2026 · DOI

• 1. Agent-based simulation. Implement the six-level model in an agent-based sim- ulation with heterogeneous α distributions, iterated interactions, and selectable governance architectures (Leviathan vs. platform). This would allow quantitative testing of the Leviathan Paradox under varying conditions.

  Cooperation as Attractor: A Multi-Level Formal Refutation of Hobbes's Bellum Omnium Contra Omnes · 2026 · DOI

• The paper predicts that cooperative equilibria with exactly two cooperating players (Q=2) may only exist under DamRed and only for sufficiently risk-averse subjects, yet no analysis of actual observed equilibrium coordination on specific Q values is provided, nor experimental conditions designed to investigate which Qmin thresholds subjects actually implement.

  Cooperative protection against stochastic losses: Experimental evidence on behavioral dynamics · 2026 · DOI

• Probability weighting effects in the ProbRed treatment are discussed theoretically (footnote 23) as potentially reducing cooperation due to the flat weighted probability function in the 10-50% probability range, but no experimental manipulation isolating the effect of probability weighting from standard probability treatment is conducted to directly test this mechanism.

  Cooperative protection against stochastic losses: Experimental evidence on behavioral dynamics · 2026 · DOI

• The prospect theory predictions regarding risk-loving behavior in loss settings (footnote 23) suggest differential cooperation patterns between DamRed and ProbRed for risk-averse versus risk-loving subjects, but the paper provides no empirical measurement of individual risk preferences or categorization of subjects by risk attitude to test whether observed cooperation rates align with predicted heterogeneous responses.

  Cooperative protection against stochastic losses: Experimental evidence on behavioral dynamics · 2026 · DOI

• The impulse balance learning model (Appendix B) predicts that cooperation should be phased out at similar rates in DamRed1 and DamRed due to identical average payoff differences (3 per period), but this prediction requires experimental validation comparing actual decay trajectories of cooperation over time between these two treatments to test whether the model's assumptions about reinforcement mechanisms hold.

  Cooperative protection against stochastic losses: Experimental evidence on behavioral dynamics · 2026 · DOI

• The analytical solution for Qmin under CRRA risk preferences proves impossible to derive; the paper relies entirely on simulation results (Figure 3) for the three treatments (DamRed1, DamRed, ProbRed). Closed-form analytical expressions for the cooperation thresholds as functions of risk aversion parameter σ across these treatments need to be developed to provide theoretical grounding beyond numerical simulations.

  Cooperative protection against stochastic losses: Experimental evidence on behavioral dynamics · 2026 · DOI

• Translation to the laboratory: chemostats, microfluidic setups, and batch cultures. Our modelling approach is mainly inspired by chemostat setups, which are commonly used in laboratory-controlled experiments to modulate the influx of nutrients and drugs in microbial communities. In such systems, the concentrations of resources and toxins can be adjusted to impose harsh conditions that generate population bottlenecks, whose eco-evolutionary impacts are the subject of intense study [25,88,93]. Here, we focus on the biologically relevant regime of intermediate environmental time variation [25,94,119], characterised by ν ≲ 1 and 0 carrying capacity, whereas the local composition (number of S and R cells in a deme) relaxes more slowly, on a timescale δ ≲ 1, in which the population size within each deme rapidly tracks the ≤ 1/s with typically s ≲ 10–1 (s = 0.1 in all figures here; see “Background” in Model & Methods and S1 Appendix Sec. ∼ 1.2.1). This regime corresponds to conditions fluctuating between mild (K = K+) and harsh (K = K–) environmental states with a frequency between once per hour and once per day, that is, approximately every 1 – 100 microbial generations (ν = 0.01 – 1; see Model & Methods). The drug influx is kept constant, and each environmental switch, theoretically treated as instantaneous, occurs rapidly in practice. While we have conveniently represented the switching of the carrying capacity as a random process at rates ν 1/ν+ + 1/ν–, would not change the qualitative results of our study (“Background” in Model & Methods, S1 Appendix Sec. 1.2.3), and could be seen as a potential laboratory implementation of this model. (Fig 1A), the case where K varies periodically between K+ and K–, with period ± Since all the above conditions can be practically implemented [25,94], we believe that our theoretical predictions can, in principle, be probed in prospective laboratory-controlled experiments. The environmental switching of PLOS Computational Biology | https://doi.org/10.1371/journal.pcbi.1013997 March 16, 2026 22 / 31 K(t) would be realised using a sequence of spatially connected, fixed-volume chemostats, each acting as a deme, see, e.g., Ref.. The rate of cell migration would be set by the rate of volume exchange between neighbouring demes-chemostats (0.001% – 10% of the volume every hour). Moreover, with microfluidic devices and single-cell techniques, it is possible to perform spatially structured experiments involving as few as 10 – 100 cells per microhabitat patch [9,107,149]. These conditions are consistent with our modelling parameters, notably those corresponding to demes of relatively small size under harsh conditions (e.g., K = K– = 80). The migration rate between microhabitats in such setups largely depends on the experimental design (e.g., number of patch-to-patch channels, channel cross-section).

  Slow spatial migration can help eradicate cooperative antimicrobial resistance in time-varying environments · 2026 · DOI

• Although rapid changes in the food web structure through adaptive foraging behavior can confer stability to complex food webs, as reported by Kondoh (Science 299:1388–1391, ), the exact mechanisms behind this adaptation have not been specified in previous studies; thus, the applicability of such predictions to real ecosystems remains unclear.

  Effects of evolutionary changes in prey use on the relationship between food web complexity and stability · 2010 · DOI

• In short, the argument is set forth that animals, by and large, do not kill or seriously injure members of their own species because it usually is not in their genetic self-interest to do so; social patterns of interaction such as aggressive encounters should be examined in terms of their effects on the fitness of the individuals engaging in the behaviors before group adaptations are simply assumed.

  The evolution of aggression and the level of selection controversy · 1980 · DOI

• This trade-off leads young learners to learn preferentially from relatively young exemplars, who are common and still able to provide substantial amounts of novel knowledge, given learners limited knowledge at early ages.

  When to learn from elders or peers: accessibility-knowledge trade-offs explain diversity in age-biased social learning · 2026 · DOI

• The rate at which rewards are given and how rewards are distributed among contributors is likely to affect the occurrence of public goods production, but empirical evidence is contradictory.

  Reward inequity can promote both public goods production and free riding · 2026 · DOI

• However, the broader utility of this approach remains limited by an incomplete understanding of how selective pressures imposed by antimicrobials interact with other environmental factors to shape the emergence and persistence of resistance.

  Environmental heterogeneity facilitates competitive suppression of drug resistance · 2026 · DOI

• Apparent exceptions to this principle occur primarily when problems are sufficiently simple that they can be solved by mere trial and error or when the incentives of team members are insufficiently aligned.

  Maintaining Transient Diversity Is a General Principle for Improving Collective Problem Solving · 2023 · DOI

• Recent observations of chaos in populations or communities have shown that LEs vary by at least two orders of magnitude, yet the factors underlying this variability remain unclear.

  Allometric scaling of Lyapunov exponents in chaotic populations · 2020 · DOI

• Focusing on the direct reciprocity strategies of Tit-for-Tat and Win-stay/Lose-shift and the indirect reciprocity strategies of Cooperative Reputation and Tag, Tit-for-Tat and Cooperative Reputation are found to be robust, while Tags have mixed results.

  International Cooperation: Testing Evolution of Cooperation Theories · 2017 · DOI

• The issue, known as network reciprocity, of whether population structure can foster cooperative behavior in social dilemmas has been addressed by many, but theoretical studies have yielded contradictory results so far—as the problem is very sensitive to how players adapt their strategy.

  How Evolutionary Dynamics Affects Network Reciprocity in Prisoner’s Dilemma · 2015 · DOI

• While there is an extensive literature on the theory of infinitely repeated games, empirical evidence on how “the shadow of the future” affects behavior is scarce and inconclusive.

  Cooperation under the Shadow of the Future: Experimental Evidence from Infinitely Repeated Games · 2005 · DOI

• In general, human evolutionary psychology and evolutionary game theory provide useful frameworks for thinking about behavioral strategies, such as Machiavellianism, and identify a large number of specific hypotheses that have not yet been tested by personality and social psychologists.

  Machiavellianism: A synthesis of the evolutionary and psychological literatures. · 1996 · DOI

• A further study of secondary rein- forcement and the discrimination hypothesia. A further study of reinforcement effect within subjects.

  Partial Reinforcement Effects On Vigor and Persistence · 1967 · DOI

• Although many studies of competition were already made, some of them, we found, were lacking in sufficient conditional analysis of competitive situation, others made no comparison with control groups, still others neglected statistical validation.

  EXPERIMENTAL STUDIES OF COMPETITION · 1951 · DOI

Most-cited papers in Evolutionary Game Theory and Cooperation

• The ecology of the microbiome: Networks, competition, and stability · Science · 2015 · 2,541 citations
• Cooperation under the Shadow of the Future: Experimental Evidence from Infinitely Repeated Games · American Economic Review · 2005 · 453 citations
• Machiavellianism: A synthesis of the evolutionary and psychological literatures. · Psychological Bulletin · 1996 · 411 citations
• Experimental Games and Social Decision Making · Annual Review of Psychology · 2020 · 185 citations
• Evolution of prosocial behaviours in multilayer populations · Nature Human Behaviour · 2022 · 115 citations
• Reinforcement learning and collective cooperation on higher-order networks · Knowledge-Based Systems · 2024 · 89 citations
• Strategy evolution on higher-order networks · Nature Computational Science · 2024 · 86 citations
• Evolutionary dynamics of any multiplayer game on regular graphs · Nature Communications · 2024 · 79 citations
• Explosive Cooperation in Social Dilemmas on Higher-Order Networks · Physical Review Letters · 2024 · 76 citations
• Revisiting the form and function of conflict: Neurobiological, psychological, and cultural mechanisms for attack and defense within and between groups · Behavioral and Brain Sciences · 2018 · 75 citations

Most recent work

• Social structure as a form of collective intelligence: a new framework · Philosophical Transactions B · 2026
• Community coalescence reveals strong selection and coexistence within species in complex microbial communities · bioRxiv · 2026
• A brief review of evolutionary game dynamics in the reinforcement learning paradigm · Communications in Theoretical Physics · 2026
• Slow spatial migration can help eradicate cooperative antimicrobial resistance in time-varying environments · PLOS Computational Biology · 2026
• Cooperative protection against stochastic losses: Experimental evidence on behavioral dynamics · Journal of Evolutionary Economics · 2026
• Cooperation as Attractor: A Multi-Level Formal Refutation of Hobbes's Bellum Omnium Contra Omnes · Zenodo (CERN European Organization for Nuclear Research) · 2026
• A spatiotemporal cell theory for cooperative pattern formation in reinforcement learning-driven evolutionary games. · Chaos: An Interdisciplinary Journal of Nonlinear Science · 2026
• Strategy Dynamics of Three-Strategy Snowdrift Game Induced by Reward Strategy and Payoff Delay · Journal of Mathematics and Interdisciplinary Applications · 2026
• Dissimilarity measures for generalized Lotka-Volterra systems on networks · Scientific Reports · 2026
• How Demographic Noise Shapes Phenotypic Clusters in Environmental Gradients · bioRxiv · 2026

Related topics in Social Sciences