Decision analysis is an explicit, quantitative and prescriptive means by which the physician can identify optimal clinical strategies under conditions of uncertainty. It is incomplete, however, since it dispenses clinical advice without regard for the fact that the patient--for whatever reason--might choose to reject that advice. Game theory provides a supplementary means to explicate optimal rational strategies in situations where the actual outcome depends on the choices of both the patient and the physician. To determine its potential clinical relevance, we used game theory to reassess a clinical problem which has been used as a textbook exemplar of decision analysis: Should patients with chronic liver failure undergo liver biopsy before being treated? Decision analysis prescribes a pure (deterministic) strategy: the physician should always perform a biopsy. In contrast, given the proper conditions, game theory mandates a mixed (probabilistic) strategy: the physician should (randomly) recommend biopsy to only some fraction of patients, and only some fraction of these should (randomly) accept this advice. Thus, whenever the patient is free to accept or reject the physician's advice, game theory provides a prescriptive decision-making model which is qualitatively and quantitatively different from decision analysis.