Inclusive groups can avoid the tragedy of the commons

The study addresses how to overcome the tragedy of the commons in public goods games, where defectors earn higher payoffs than contributors despite mutual cooperation yielding the highest group benefit. Prior mechanisms promoting cooperation include reciprocity, green beard effects, spatial structure, and costly punishment. The authors explore whether coupling an individual’s payoff to group success via redistribution (termed inclusiveness) can incentivize cooperation without incurring punishment costs. They introduce a continuous parameter, selfishness ζ, where inclusiveness equals 1 − ζ: a fraction ζ of each player’s payoff remains individual, while fraction 1 − ζ is pooled and equally redistributed. This links individual outcomes to group performance even though reproduction remains at the individual level, distinct from strict group-level selection. The research questions are: (1) Does inclusiveness lower the threshold for cooperation in public goods games? (2) How does inclusiveness interact with costly punishment? The work is motivated by potential policy analogs such as a conditional basic income linked to group or societal economic success.

The paper situates its contribution within extensive research on cooperation in social dilemmas. It references classic work on the tragedy of the commons and mechanisms fostering cooperation: reciprocity, green beard effects, punishment (including human and non-human forms), and spatial interactions. Concepts such as kin selection, multilevel selection, and inclusive fitness are discussed as related but distinct frameworks affecting cooperation; however, the study explicitly does not model kin structure or group reproduction. Prior work has considered pooling resources to enable group-level selection effects in public goods games, but fractional redistribution via a tunable selfishness parameter has not been analyzed in this context.

Analytical model: The authors extend the standard public goods game with group size k+1, synergy factor r, and optional punishment (fine β, cost γ) by introducing a selfishness parameter ζ in [0,1]. Fraction ζ of individual payoffs remains with individuals, while fraction 1 − ζ of net earnings is pooled and equally redistributed. Without punishment (β = γ = 0), closed-form expressions for cooperator and defector payoffs are derived as functions of r, ζ, k, and the number of cooperating peers. A critical synergy threshold r_c at which cooperation becomes favorable is obtained; inclusiveness (lower ζ) reduces r_c relative to the classical game (ζ = 1). With punishment, they incorporate fines imposed by punishers (moralists and immoralists) on defectors (defectors and immoralists) and costs borne by punishers per defecting peer. Immoralists do not self-punish. Using the density of punishers pp, they derive an expression for the cooperation threshold r_c that depends on β, γ, ζ, pp, and k, showing how inclusiveness and punishment jointly affect the critical point. Punishment also reduces group net earnings, implicitly penalizing all players through the redistribution channel when ζ < 1. Computational evolutionary model: To validate analytical predictions under evolutionary dynamics with stochastic mutations, the authors implement an agent-based evolutionary simulation (following Hintze 2015 with modified payoffs). Each agent carries two genes: probability to cooperate (p_c) and probability to punish (p_p). Agents are grouped to play the public goods game; payoffs determine reproductive success. Offspring inherit parental probabilities with mutations. Payoff distribution is governed by ζ, with ζ = 1 reproducing the classic game and ζ = 0 yielding full pooling of net earnings. Parameter sweeps: Without punishment (β = γ = 0), they vary r from 3.0 to 6.0 in steps of 0.2 and ζ from 0.0 to 1.0 in steps of 0.1. For each parameter combination, they run 100 independent replicates for 100,000 generations, reconstruct the line of descent, and average the final 100 generations to estimate convergence values of p_c and p_p. With punishment, they test six combinations increasing β from 0.0 to 1.0 while decreasing γ from 1.0 to 0.0, using the same evolutionary protocol. Additional sweeps vary β and γ jointly at selected r and ζ to compare their influence on the cooperation threshold.

• Inclusiveness lowers the cooperation threshold: In simulations without punishment, for ζ = 1 (classical game) cooperation emerges around r ≈ k+1 (with k = 4, threshold at r ≈ 5), while decreasing ζ shifts the critical synergy r downward, enabling cooperation at lower r. This matches the analytical prediction that inclusiveness (lower ζ) reduces the required synergy for cooperation.
• Interaction with punishment: Analytical results show the critical synergy r_c decreases with higher punishment fines β, lower punishment costs γ, and lower ζ (more inclusiveness), and depends on punisher density pp. Simulations confirm that increasing β and decreasing γ facilitate cooperation and that inclusiveness synergizes with punishment to further reduce the threshold.
• Fines matter more than costs: Both the analytical expression for r_c and the agent-based experiments indicate that changes in fine β have a stronger effect on the cooperation threshold than equivalent changes in cost γ. Achieving the same shift in r_c requires larger adjustments in γ than in β.
• Drift of punishment when unused: In regimes where cooperation becomes ubiquitous and punishment is not exercised (e.g., high inclusiveness or free punishment), the punishment gene p_p drifts around 0.5 due to neutrality.
• Free or low-cost punishment and high inclusiveness both promote full cooperation: When punishment becomes costless (γ = 0), simulations produce universal cooperation. Similarly, sufficiently inclusive redistribution strongly promotes cooperation, reducing dependence on punishment to achieve cooperative equilibria.

The findings demonstrate that coupling individual payoffs to group success through inclusive redistribution is a powerful mechanism to resolve the social dilemma in public goods games. By lowering the effective threshold for synergy needed to sustain cooperation, inclusiveness can either complement or, in many regimes, substitute for costly punishment. The interaction term shows that punishment remains effective, especially with higher fines and lower costs, but inclusiveness generally exerts a stronger and broader pro-cooperative effect. Moreover, any punishment regime that reduces group net earnings implicitly penalizes all group members under redistribution, highlighting societal trade-offs when implementing punitive measures. The results suggest policy analogs where redistributing a portion of gains (e.g., via a conditional basic income linked to group or societal performance) aligns individual incentives with collective welfare, thereby mitigating the tragedy of the commons.

The study introduces a tunable inclusiveness mechanism in the public goods game that redistributes a fraction of net earnings among group members, effectively coupling individual payoffs to group success. Analytical derivations and agent-based evolutionary simulations show that inclusiveness significantly lowers the synergy required for cooperation and interacts synergistically with punishment, with fines exerting a stronger influence than costs. The work implies that appropriately designed redistribution—akin to a conditional basic income tied to the economic success of the whole—can foster widespread cooperation and lessen reliance on costly punishment. Many alternative redistribution mechanisms could implement similar principles in practice.

• The analytical framework assumes infinite populations and mean-field behavior.
• The evolutionary model implements individual-level reproduction; strict group reproduction is not modeled.
• The study explicitly does not include kin structure, kin selection, or multilevel selection mechanisms.
• Model-specific assumptions include that immoralists do not self-punish and that punishment fines and costs are applied as specified before redistribution, which reduces group net earnings.