This is a phase I/II open label study being conducted to evaluate the overall safety and initial effectiveness of an investigational drug, Eltrombopag in patients who are 60 years of age and older and who have Acute Myelogenous Leukemia (AML). Eltrombopag is an investigational drug, which means it has not been approved by the U.S. Food and Drug Administration (FDA) for use in this type of disease. Approximately 35 people will be enrolled on this study at the University of Pennsylvania