A coevolution model of defensive medicine, litigation and medical malpractice insurance

We model the interactions between physicians and patients, subject to clinical and legal risks, by means of an evolutionary game. In each instant of time, there is a large number of random pairwise encounters between members of the two populations. In each encounter, a physician heals a patient. The outcome of the healing process is uncertain and may result in patient harm; if that happens, the patient may sue the physician for medical malpractice. Physicians have to choose between two alternative treatments, D and ND, with different levels of benefits and risks. The treatment D is less risky than the alternative treatment ND, but has the disadvantage of providing a lower expected benefit to the patient. Therefore its provision corresponds to practicing “negative” defensive medicine. Physicians prevent, at least partially, negligence charges by buying medical malpractice insurance. This transfers the risk of litigation from the physician to the insurer. The dynamics we analyze are determined by a three-dimensional discrete-time dynamic system, where the variables x and y are, respectively, the shares of defensive physicians and litigious patients, while the variable a represents the insurance premium. In such a context we show that, depending on the policy's price calculation principle as well as on model's parameters related to the accuracy of the judicial system and legal reforms, the game's final outcome could be an appealing equilibrium point in which the defensive strategy of physicians and litigious behavior of patients vanish, an interior (Nash) equilibrium in which all strategies coexist, or even an oscillatory behavior arisen via a Neimart–Sacker bifurcation in which strategies coexist in a recurrent manner. Furthermore, we state a “no chaos” conjecture, supported by analytical, numerical and empirical arguments.