A Study to Evaluate the Safety and Efficacy of Nivolumab Monotherapy and Nivolumab in Combination With Ipilimumab in Pediatric Participants With High Grade Primary Central Nervous System (CNS) Malignancies

Inclusion Criteria:

* Must have received standard of care therapy, and there must be no potentially-curative treatment available, in one of the following cohorts:
* A newly diagnosed Diffuse Intrinsic Pontine Glioma (DIPG) that has been treated with radiation therapy (RT) but no chemotherapy
* A histologically confirmed recurrent or progressive non-brainstem High Grade Glioma (HGG) previously treated with surgical resection and RT
* A histologically confirmed medulloblastoma that has relapsed or is resistant to at least one line of prior therapy including surgery, RT, and chemotherapy
* A histologically confirmed ependymoma that has relapsed or is resistant to at least one line of prior therapy including surgical resection and RT
* A histologically-confirmed high grade CNS malignancy "other than above" which is recurrent or progressive after at least one line of prior therapy
* Lansky play score (LPS) for ≤ 16 years of age or Karnofsky performance scale (KPS) for \> 16 years of age assessed within two weeks of enrollment must be \>= 60
* A tumor sample must be available for submission to central laboratory (not required for DIPG)

Exclusion Criteria:

* An active, known, or suspected autoimmune disease
* A concurrent condition requiring systemic treatment with either corticosteroids or other immunosuppressive medications within 14 days of start of study treatment
* Known history of positive test for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS).

Other protocol defined inclusion/exclusion criteria apply