Single Rising Dose Study of MK-8723 in Healthy Participants and Participants With Immune Thrombocytopenia Purpura (MK-8723-001)

Inclusion Criteria (Part 1): * Female participants must be non-pregnant, non-breast feeding, and of non-childbearing potential * Has a Body Mass Index (BMI) \<=32 kg/m\^2 * Has a body weight \>= 50 kg and \<= 100 kg * Has been judged to be in good health based on medical history, physical examination, vital sign measurements, electrocardiogram (ECG), and laboratory safety tests * Non-smoker or has not used nicotine or nicotine-containing products for at least 3 months Inclusion Criteria (Part 2): * Has been diagnosed with ITP at least 3 months prior * Female ITP participants must be non-pregnant, non-breast feeding, and either of 1) non-childbearing potential or 2) must have serum beta human chorionic gonadotropin (HCG) level consistent with a non-pregnant state, and agree to use acceptable contraception from pretrial period until 84 days postdose * Has a BMI \<=36 kg/m\^2 * Has been judged to be in good health, other than ITP diagnosis, based on medical history, physical examination, vital sign measurements, ECG, and laboratory safety tests Exclusion Criteria (Part 1): * Has a history or clinically significant endocrine, gastrointestinal, cardiovascular, hematological, hepatic, immunological, renal, respiratory, genitourinary, or major neurological abnormalities or diseases * Has a history of cancer (malignancy) * Has a history of significant multiple and/or severe allergies or has had an anaphylactic reaction or significant intolerability to prescription or non-prescription drugs or food * Is positive for hepatitis B surface antigen, hepatitis C antibodies, or human immunodeficiency virus (HIV) * Has had major surgery or donated or lost 1 unit of blood in the 4 weeks prior * Has participated in another investigational trial within 4 weeks (12 weeks for biologics) * Has received a live virus vaccination within 42 days or plans to receive such while participating in the trial * Is unable to refrain from or anticipates the use of any medication, including prescription and non-prescription drugs and herbal remedies from 2 weeks prior and for the duration of the trial * Consumes greater than 3 glasses of alcoholic beverages per day * Consumes greater than 6 servings of caffeine-containing beverages per day * Is currently a regular user of any illicit drugs or has a history of drug and/or alcohol abuse within 3 months * Has a history of ITP or other autoimmune disease * Has an active infection that is clinically significant Exclusion Criteria (Part 2): * Has a comorbid and significant hematological or immunological disorder * Has a history of significant multiple and/or severe allergies or has had an anaphylactic reaction or significant intolerability to prescription or non-prescription drugs or food * Is positive for hepatitis B surface antigen, hepatitis C antibodies, or HIV * Has had major surgery or donated or lost 1 unit of blood within 4 weeks * Has participated in another investigational trial within 4 weeks (12 weeks for biologics), excluding prior participation in the current study * Has a history of ITP unresponsive to intravenous immunoglobulin (IVIG) * Has had systemic corticosteroid use within 1 month (with the exception of stable low dose oral corticosteroids) * Has had systemic IVIG or other systemic immunomodulatory therapy, excluding MK-8723 administration in the current study, within 3 months * Has received a thrombopoietin receptor antagonist within 3 months * Is unable to refrain from using thrombopoietin receptor agonists and/or systemic immune modulatory medications throughout the study * Has received a live virus vaccine within 42 days prior or plans to receive such during the trial * Consumes greater than 3 alcoholic beverages per day * Consumes greater than 6 servings of caffeine-containing beverages per day * Is currently a regular user of any illicit drugs or has a history of drug and/or alcohol abuse within 3 months * Has clinical evidence of bleeding or coagulopathy including petechial rash, easy bruising, or excessive gingival bleeding with routine dental hygiene * Has an active infection that is clinically significant