For more information regarding Bristol Myers Squibb Clinical Trial participation, please visit www.BMSStudyConnect.com Inclusion Criteria: - Histologic confirmation of adenocarcinoma of the prostate and evidence of stage IV disease - Must have ECOG performance status 0-1 - Documented prostate cancer progression per PCWG3 criteria within 6 months prior to screening - Ongoing androgen deprivation therapy (ADT) with a gonadotropin-releasing hormone (GnRH) analogue or bilateral orchiectomy - Participants who are chemotherapy-naive and received 1 to 2 prior second generation hormonal therapies - Sufficient tumor sample from fresh or archival tumor tissue obtained no more than 1 year prior to enrollment, from a metastatic lesion or primary tumor lesion that has not been previously irradiated Exclusion Criteria: - Participants with active brain metastases - Prior malignancy active within the previous 3 years except for locally curable cancers that have been apparently cured - Participants with an active, known, or suspected autoimmune disease - Participants requiring systemic treatment with corticosteroids (> 10 mg daily prednisone equivalent) or other immunosuppressive medications - Prior treatment with anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CTLA-4, or any antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways - Prior treatment with docetaxel or another chemotherapy for metastatic castration resistant prostate cancer Other protocol defined inclusion/exclusion criteria could apply