Social norms are often characterized as a system of rules that guide behavior. However, social norms also allow for flexibility; not entirely restricting individuals to one possible behavior. Here, we put forward an agent-based cognitive model that captures social norms as processes that are socially constructed through interactions between individuals. In this modelling work, we focus on the role of norm acquisition and conformity bias in both action production and inference-making. This computational cognitive model allows us to think about social norms along three dimensions: individual vs. collective, behavior vs. belief, and subjective vs. objective. Our simulation results show that increased conformity bias can induce misjudgments about the true desires of others and misalignment between different agents' perceptions of the social norm. However, if agents do not assume that others also conform in their behavior, this increased conformity bias does not necessarily lead to excessive misperceptions of the social norm.