Evolution of cooperation in spatial heterogeneous social dilemmas with dynamic self-adaptive matching

From the perspective of real-world interaction scenarios, the assumption of monotypic social dilemma engagement or fixed role allocations within heterogeneous social dilemmas contexts fundamentally misrepresents the dynamics of human social cognition. Empirical evidence consistently suggests that behavioral plasticity is achieved through adaptive identity switching across heterogeneous social dilemma environments. Herein, we develop an evolutionary game model simultaneously encompassing multiple social dilemmas (prisoner's dilemma game and snowdrift game), wherein agents engage in polymorphic game-environment governed by their own adaptive characteristic. Specifically, during the strategy update phase, if the agent $x^{\prime }s$ current strategy is retained, its strategy stickiness ${\theta }_x$ increases one unit; otherwise, the metric reverts to the initial value of 0. Additionally, if ${\theta }_x$ reaches the maximum value of 100, it signifies the termination of the old agent and the initialization of a new one, with the metric also reverting to 0. Moreover, agent whose strategy adherence is beyond predefined threshold ${\theta }_{th}$ is classified as possessing strong social dilemma resolution capacity, while that is below the threshold is allocated to mild-conflict scenarios. Subsequently, through sufficient Monte Carlo simulation, we systematically investigate the evolutionary trajectories and stable-state characteristics of cooperation in dynamically adaptive multi-social dilemma systems, yielding several insightful findings.