Inclusion Criteria:

          -  Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status: 0,
             1, or 2 (However, those patients with a performance state of 3 because they are wheel
             chair bound due to congenital or traumatic events more than one year before the
             diagnosis of Merkel cell carcinoma are eligible).

          -  Women must not be pregnant or breast-feeding due to the unknown effects of the study
             drug in this setting. All women of childbearing potential must have a blood test or
             urine study within 2 weeks prior to registration to rule out pregnancy. A female of
             childbearing potential is any woman, regardless of sexual orientation or whether they
             have undergone tubal ligation, who meets the following criteria: 1) has achieved
             menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy;
             or 3) has not been naturally postmenopausal (amenorrhea following cancer therapy does
             not rule out childbearing potential) for at least 24 consecutive months (i.e., has had
             menses at any time in the preceding 24 consecutive months).

          -  Women of childbearing potential, and sexually active males, on Arm A MK-3475
             (pembrolizumab must use accepted and effective method(s) of contraception or abstain
             from sex from time of registration, while on study treatment, and continue for 120
             days after the last dose of study treatment. For patients on Arm B only receiving
             radiation therapy, contraception use should be per institutional standard.

          -  Patient must have a histological confirmation of diagnosis of Merkel cell carcinoma
             (MCC), pathologic stages (American Joint Committee on Cancer [AJCC] version 8) I-IIIb.

               -  Stage I patients with negative sentinel lymph node biopsy are ineligible.
                  Patients who have a positive biopsy or for whom no biopsy was done are eligible.

               -  Patients with distant metastatic disease (stage IV) are not eligible.

               -  The primary tumor must have grossly negative margins. (Microscopically positive
                  margins are allowed).

               -  Cancers of unknown primary that have regional disease only can be included.

               -  Complete nodal dissection is not required for eligibility.

          -  Patients with all macroscopic Merkel cell carcinoma (either identified by physical
             exam or imaging) have been completely resected by surgery within 16 weeks before
             registration.

          -  All patients must have disease-free status documented by a complete physical
             examination and conventional imaging studies within 8 weeks prior to registration.

          -  Patient may not have a history of distant metastatic disease.

               -  NOTE: Loco-regional recurrent disease is acceptable, as long as this is not
                  metastatic (prior surgery with or without radiation therapy is acceptable).

          -  For patients with initial presentation of Merkel cell carcinoma, patient must have no
             previous systemic therapy or radiation therapy prior to surgery for Merkel cell
             carcinoma and cannot have completed adjuvant radiation therapy for Merkel cell
             carcinoma more than 6 weeks prior to registration. Patients actively undergoing
             radiation therapy or having completed adjuvant radiation therapy within 6 weeks of
             registration are eligible, as long as resection date is within 16 weeks of
             registration.

          -  White blood count >= 2000/uL (within 4 weeks prior to randomization).

          -  Absolute neutrophil count (ANC) >= 1000/uL (within 4 weeks prior to randomization).

          -  Platelets >= 75 x 10^3/uL (within 4 weeks prior to randomization).

          -  Hemoglobin >= 8 g/dL (>= 80 g/L; may be transfused) (within 4 weeks prior to
             randomization).

          -  Creatinine =< 2.0 x upper limit of normal (ULN) (within 4 weeks prior to
             randomization).

          -  Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 2.5 x ULN
             (within 4 weeks prior to randomization).

          -  Total bilirubin =< 2.0 x ULN, (except patients with Gilbert's syndrome, who must have
             a total bilirubin less than 3.0 mg/dL) (within 4 weeks prior to randomization).

          -  Patients who are human immunodeficiency virus (HIV)+ with undetectable HIV viral load
             are eligible provided they meet all other protocol criteria for participation.

          -  Patients with hepatitis B virus (HBV) or hepatitis C virus (HCV) infection are
             eligible provided viral loads are undetectable. Patients on suppressive therapy are
             eligible.

          -  Patients must not be on active immunosuppression, have a history of life threatening
             virus, have had other (beside non-melanoma skin cancers, or recent indolent cancers
             e.g.: resected low grade prostate cancer) invasive cancer diagnoses in the last two
             years, or have had immunotherapy of any kind within the last 2 years.

          -  Patients must not have a history of (non-infectious) pneumonitis that required
             steroids or has current pneumonitis.

          -  Operative notes from patient's surgical resection must be accessible.