This work-in-progress analyzes the method of assessing civil and criminal penalties used in the ancient Athenian courtroom (a process known as "timesis") and, in particular, examines the strategies that could be employed by litigants in order to manipulate the process. Briefly stated, when assessing a penalty after convicting a defendant, both litigants would propose a penalty and the jury would select either one proposal or the other. This paper applies game theory to examine how this procedure would have worked in practice by describing both its advantages as well as its susceptibility to manipulation by the litigants. The discussion also touches upon modern versions of this system as seen in final-offer, or “baseball,” arbitration and contemplates the operation of the system of "timesis" during the famous trial of Socrates.