Using Game Theory to Analyze Doctors’ Decision on Antibiotics
Link: https://www.nature.com/articles/s41467-021-21088-5
There are many occasions in medicine where a doctor must make life or death decisions for their patients. For example, the doctor must decide whether to give a patient a particular test, or what a patient’s symptoms mean, or if the patient should receive a particular medicine. There are often significant ramifications for these decisions, as incorrectly refraining from giving the patient a medicine can worsen their condition but giving the patient a medicine when they do not need it can also hurt them, cost the doctor/patient extra money, and/or hinder the ability of a doctor to provide later patients with this medicine. In a paper by Diamant, Baruch, et al, titled “A game theoretic approach reveals that discretizing clinical information can reduce antibiotic misuse”, the authors discuss how game theory can provide insight into whether to give a patient antibiotic.
The approach starts with defining the game, like our approach in class. In this “game”, the doctors are the players. Their playoff for giving a patient an antibiotic is completely dependent on the status of the patient (information available to the doctor and the patient’s probability of infection), not on future patients or other doctors. Thus, the strategy of the player is defined by the patient’s status, given as a density function. The authors use the concept of Nash equilibrium to show that if doctors are given complete information about the patient, doctors tend to prioritize their patient, preferring the individual over the societal optimum. However, by changing the information signal from continuous to dichotomous, meaning that instead of receiving pure numbers, the doctors are receiving categories based on a single threshold, the two Nash equilibriums converge.
This analysis has several consequences. In class, most of our analysis focuses on analyzing the results of given playoffs. We have discussed how the outcome changes when those playoffs change, or the rules of the game change. For example, changing the requirements to study for the both the exam and the presentation, instead of one or the other, changes the Nash equilibrium for the game. We have also examined socially optimal solutions, and situations where the Nash equilibrium is the same as the social optimum and situations where they are different. In the market clearing game, each buyer is getting what they want, and the total value is socially optimum. This paper expands on these concepts to describe how we can force the Nash equilibrium to coincide with the social optimum through manipulating information given to the players to change their strategies and thus the playoffs.
It is interesting to consider how those “in charge” of the game, can change it to produce the results they want. Even though every doctor is making a rational decision from their point of view, their actions are in a large part influenced by the information they receive regarding their patients, which is partly given by others. This ability can both be positive, and negative for the patients involved. On the other hand, what is the difference between a Nash equilibrium and a social optimum? In what cases do they need to be the same, and how can these rules and regulations be modified to ensure the best outcome for individual patients as well as the overall good? At what point does information hinder our ability to make the best decision?