Motivated by recent discussions about the issue of risk perceptions for climate change related events, we introduce a non-cooperative game setting where agents manage a common pool resource under a potential risk, and agents exhibit different risk perception biases. Focusing on the effect of the polarization level and other population features, we show that the type of bias (overestimation versus underestimation biases) and the resource quality level before and after the occurrence of the shift have first-order importance on the qualitative nature of behavioral adjustments and on the pattern of resource conservation. When there are non-uniform biases within the population, the intra-group structure of the population qualitatively affects the degree of resource conservation. Moreover, unbiased agents may react in nonmonotone ways to changes in the polarization level when faced with agents exhibiting different types of bias. The size of the unbiased agents' sub-population does not qualitatively affect how an increase in the polarization level impacts individual behavioral adjustments, even though it affects the magnitude of this change. Finally, it is shown how perception biases affect the comparison between centralized and decentralized management.