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Cooperation, selfishness, and dilemma are prevalent in diverse contexts, spanning from biological systems to human societies. Gaining insight into the mechanisms that facilitate and sustain cooperation is essential for effectively tackling global challenges such as climate change, resource depletion, and epidemics. This study presents a new ecological-evolutionary game theory model called the Pairwise Loner Game (PLG). The model combines the Optional Prisoner's Dilemma (OPD) and Rock-Paper-Scissors (RPS) games by incorporating an environmental feedback variable. The study alters the payoff matrices of the OPD and RPS games to guarantee compatibility and generates a comprehensive PLG payoff matrix that includes the environmental state. The replicator dynamics that govern the changes in strategy frequencies and the differential equation that describes the dynamics of the environment are established.
Numerical simulations and analyses demonstrate that the environmental influence function is pivotal in determining environmental tipping points. This function models how the environment responds to the frequencies of different strategies, which in turn affects the availability of resources and the overall stability of the system. The simulations reveal that minor changes in the environmental influence function can lead to significant shifts in tipping points, highlighting the sensitivity of the system to environmental feedback. Additionally, the presence of all three strategies—cooperators, defectors, and loners—is significant for promoting a stable and sustainable environment. Cooperators contribute to resource replenishment, defectors exploit resources, and loners abstain from interaction, creating a dynamic balance that prevents the dominance of any single strategy and supports the long-term sustainability of the environment. This intricate interplay underscores the importance of maintaining diversity in strategies to enhance the resilience of ecosystems and social systems against external shocks and internal fluctuations. |
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