The straight and narrow: A game theory model of broadand narrow-spectrum empiric antibiotic therapy

Physicians prescribe empiric antibiotic treatment when definitive knowledge of the pathogen causing an infection is lacking. The options of empiric treatment can be largely divided into broadand narrow-spectrum antibiotics. Prescribing a broad-spectrum antibiotic increases the chances of covering the causative pathogen, and hence benefits the current patient's recovery. However, prescription of broad-spectrum antibiotics also accelerates the expansion of antibiotic resistance, potentially harming future patients. We analyse the social dilemma using game theory. In our game model, physicians choose between prescribing broad and narrow- spectrum antibiotics to their patients. Their decisions rely on the probability of an infection by a resistant pathogen before definitive laboratory results are available. We prove that whenever the equilibrium strategies differ from the socially optimal policy, the deviation is always towards a more excessive use of the broadspectrum antibiotic. We further show that if prescribing broad-spectrum antibiotics only to patients with a high probability of resistant infection is the socially optimal policy, then decentralization of the decision making may make this policy individually irrational, and thus sabotage its implementation. We discuss the importance of improving the probabilistic information available to the physician and promoting centralized decision making.