We study the impact of data sharing policies on cyber insurance markets. These policies have been proposed to address the scarcity of data about cyber threats, which is essential to manage cyber risks. We propose a Cournot duopoly competition model in which two insurers choose the number of policies they offer (i.e., their production level) and also the resources they invest to ensure the quality of data regarding the cost of claims (i.e., the data quality of their production cost). We find that enacting mandatory data sharing sometimes creates situations in which at most one of the two insurers invests in data quality, whereas both insurers would invest when information sharing is not mandatory. This raises concerns about the merits of making data sharing mandatory.