We propose a game-theoretic framework to model and optimize user engagement in cooperative activities over social networks. While traditional diffusion models suggest that individuals are only influenced by their neighbors, empirical evidence shows that diffusion alone does not fully explain network evolution, and non-diffusion factors play a significant role in network growth. We model network participation and resource-sharing as strategic games involving boundedly rational players to address this gap between the analytical models and empirical evidence. Specifically, we employ Log-Linear Learning (LLL), a version of noisy best response, to capture players' decision-making strategies. By incorporating stochastic decision models like LLL, our framework integrates both diffusion and non-diffusion dynamics into network evolution dynamics. Through equilibrium analysis and simulations, we demonstrate that our model aligns with theoretical predictions from existing analytical frameworks and empirical observations across various initial network configurations. Our second contribution is a novel method for selecting anchor nodes to enhance user participation. This approach allows system designers to identify anchor nodes and compute their incentives in real time under a more realistic information requirement constraints as compared to the existing approaches. The proposed approach adapts to changing network conditions by reallocating resources from less impactful to more influential nodes. Furthermore, the method is resilient to anchor node failures, ensuring sustained and continuous network participation.