Inclusion Criteria Cohort 1:

• Received and progressed on at least 2 prior chemotherapy regimens for their advanced disease; prior regimen must have included a cisplatin and a fluoropyridine
• Human epidermal growth factor receptor 2 (HER-2/neu) negative, or, if HER2/neu positive, must have previously received treatment with trastuzumab

Inclusion Criteria Cohort 2 or 3:

• HER2/neu negative
• Has not received prior systemic anti-cancer therapy for their advanced carcinoma (systemic therapy received in the neoadjuvant and adjuvant setting does not count)

Inclusion Criteria All Participants:

• Histologically- or cytologically-confirmed recurrent or metastatic gastric or gastroesophageal junction adenocarcinoma that is considered incurable by local therapies
• Willing to provide tissue for PD-L1 biomarker analysis from newly-obtained and/or archival tissue
• Measurable disease based on Response Evaluation Criteria in Solid Tumors version 1.1 (RECIST 1.1)
• Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
• Female participants of childbearing potential should have a negative pregnancy test and be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication (180 days for participants receiving cisplatin + 5FU)
• Male participants should agree to use an adequate method of contraception starting with the first dose through 120 days after the last dose of study medication (180 days for participants receiving cisplatin + 5FU)
• Adequate organ function

Exclusion Criteria:

• Currently participating and receiving study therapy or participated in a study of an investigational agent and received study therapy or used an investigation device within 4 weeks of the first dose of study medication
• Active autoimmune disease that has required systemic treatment in past 2 years
• Immunodeficiency or receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of study medication
• Prior anti-cancer monoclonal antibody (mAb) within 4 weeks prior to study Day 1 or not recovered from adverse events due to agents administered more than 4 weeks earlier
• Prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study Day 1 or who has not recovered from adverse events due to a previously administered agent
• Known additional malignancy that is progressing or requires active treatment excepting basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer
• Known active central nervous system (CNS) metastases and/or carcinomatous meningitis
• Known history of, or any evidence of active, non-infectious pneumonitis
• Active infection requiring systemic therapy
• Psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the study
• Pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the screening visit through 120 days after the last dose of study medication (180 days for participants receiving cisplatin + 5FU)
• Prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent, or previously participated in Merck pembrolizumab (MK-3475) clinical trials
• Human immunodeficiency virus (HIV)
• Hepatitis B or C
• Received live vaccine within 30 days of planned start of study medication