The co-evolution of conditional cooperation and social norms has garnered significant attention, yet the underlying mechanisms remain elusive. Social norms result from empirical expectations, individual expectations of group behavior, and normative expectations, the population's expectations of individual behavior. Aligning these expectations aids in norm formation, but diverse individual reactions to observed behavior and their sensitivity to norm conformity can be challenging. In our study, the agents are initially endowed with diverse conditional expectations, which mirror their anticipations regarding group behavior and their inherent inclination to conform to social norms, indicative of their sensitivity to psychic costs. These agents engage in a repeated public goods game, where their decisions to cooperate are shaped by their conditional expectations and the observed levels of cooperation within their group. Concurrently, free riders experience psychic costs determined by the overall level of cooperation, contribution costs, and the individual's inclination to adhere to social norms. Remarkably, our simulations unveil that agents commencing with random conditional expectations and a propensity to conform to norms can adapt to lower conditional expectations and moderate their propensity to conform to norms when initial cooperation levels are high and the contribution cost is reduced. Interestingly, increasing contribution costs intensify the population's response to norm enforcement, but this doesn't always result in a corresponding increase in cooperation. By incorporating population diversity and accounting for empirical and normative expectations within our model, we gain valuable insights into the intricate relationship between conditional cooperation and the emergence of social norms.
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