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Environmental switching between punishment and withdrawal reshapes cooperation

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  • Hasan, Mehedi
  • Kabir, K․M․Ariful

Abstract

Conflicts between individual incentives and collective welfare pose a fundamental challenge to the persistence of cooperation in social–ecological systems. Here, we develop an environment-dependent evolutionary game model in which cooperation, defection, punishment, and voluntary withdrawal co-evolve with a dynamically changing environment that shifts between depleted and replenished states. Our results show that cooperation is shaped not by any single factor, but by the strength of environmental feedback and the type of social dilemma operating when resources are scarce. When resource regeneration is weak, cooperation tends either to collapse or to persist only in simple, stable configurations largely dictated by the depleted state. In contrast, strong environmental feedback can generate sustained coexistence of strategies and even cyclical dynamics driven by mutual reinforcement between behavior and resource conditions. Notably, we find that the game structure under resource depletion plays a decisive role in determining long-term outcomes even when replenished conditions appear favorable to cooperation. Punishment and voluntary withdrawal can promote cooperation, but only when their costs and benefits align with the underlying dilemma and the rate of environmental recovery. Overall, our findings demonstrate that environmental feedback fundamentally reshapes social dilemmas, determining whether cooperation fails, stabilizes, or fluctuates over time, and provide actionable insight for designing policies that sustain collective action in complex adaptive systems.

Suggested Citation

  • Hasan, Mehedi & Kabir, K․M․Ariful, 2026. "Environmental switching between punishment and withdrawal reshapes cooperation," Applied Mathematics and Computation, Elsevier, vol. 524(C).
  • Handle: RePEc:eee:apmaco:v:524:y:2026:i:c:s0096300326000949
    DOI: 10.1016/j.amc.2026.130042
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