Hospital Competition Act of 2019 This bill establishes a series of programs and requirements relating to hospital costs, payments, and infrastructure. Among other things, the bill requires hospitals, as a condition of Medicare participation, to (1) in the case of hospitals that meet specified market concentration thresholds, apply Medicare reimbursement rates regardless of whether the individual receiving services is entitled to or enrolled in Medicare; and (2) publish the prices charged for specified services that are highly utilized. The bill also repeals (1) performance incentives under the Medicare Shared Savings Program for accountable care organizations, and (2) provisions under the Stark law (i.e., the Physician Self-Referral Law) that prohibit physician-owned hospitals from expanding facility capacity.