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Recovering cooperation in Spatial Prisoner’s Dilemma via a forced Loner mechanism

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  • Qin, Yihang
  • Chen, Hao
  • Wang, Lin

Abstract

Cooperation is a fundamental organizing principle in biological and social systems. However, under resource constraints, cooperative behavior often collapses as defectors always gain resources unilaterally in interactions. To address this, we propose a Forced Loner Mechanism (FLM) integrated into the Spatial Prisoner’s Dilemma with resource dynamics (SPDL), where bankrupt agents are forced to withdraw and receive a guaranteed subsidy. This mechanism models realistic social subsidies or industrial safety nets. Simulation results indicate that the forced loner mechanism restores cooperation under high temptation to defect. This mechanism significantly improves the overall performance of the game system by enhancing efficiency, sustainability, and fairness. These properties are quantified by three macroscopic indicators: net output, average cumulative resources, and the Gini coefficient, respectively. Moreover, a sensitivity analysis reveals that the mechanism is robust against variations in the Loner payoff. These findings provide a quantitative understanding of how social exit and protection mechanisms can be interventions to stabilize cooperation in resource-limited systems.

Suggested Citation

  • Qin, Yihang & Chen, Hao & Wang, Lin, 2026. "Recovering cooperation in Spatial Prisoner’s Dilemma via a forced Loner mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 685(C).
    • Handle: RePEc:eee:phsmap:v:685:y:2026:i:c:s0378437126000452
    DOI: 10.1016/j.physa.2026.131309
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