Managing near-miss reporting in hospitals: The dynamics between staff members’ willingness to report and management’s handling of near-miss events

•The dynamics between staff and management regarding near-miss reporting is modeled.•Willingness to report is modeled as either a known parameter or a random variable.•Strategic and Evolutionary games are developed and discussed.•The rate of reporting is obtained as an outcome at equilibrium or stable points.•The rate of reporting at equilibrium does not depend on willingness to report.