(AP Photo/Kevin Wolf)

A young man with a rattling cough shows up at the doctor's office. Sick and tired of feeling sick, he demands antibiotics.

The doctor explains that the patient has acute bronchitis that is almost certainly caused by a virus. That cough won't respond to antibiotics, the doctor says, but the patient persists.

Eventually, the doctor goes ahead and writes the prescription. Maybe it's because she knows the patient will just keep seeking second opinions until he gets the treatment he wants. Maybe it's because there are new policies in place that means physicians are being evaluated partly based on patient satisfaction. Maybe the doctor orders unnecessary tests to rule out a bacterial infection.

The patient is happy and the doctor can move on to the next patient. But both decisions are far from ideal for the patient, the doctor and for society: The drugs don't address the patient's problem, and the prescription contributes to a global crisis of emerging superbugs triggered by the overuse of antibiotics.

Modern health care, a team of physicians and a mathematician argued earlier this year in the European Journal of Clinical Investigation, is moving toward a classic economic conundrum in game theory in which the rational, self-interested choices of the patient and the doctor will frequently result in the wrong societal outcome -- either overtreatment or undertreatment. In their paper, the researchers used game theory to model the typical doctor-patient interaction and found that treatment decision mistakes are made 42 percent of the time due to such conflicting interests.

"These numbers, the 42 percent, are kind of our best guess of what might be happening, and obviously there’s uncertainty about that. It can get better and it also can get worse. I think it’s indicative of what the situation is now," said John Ioannidis, a professor of disease prevention at Stanford University School of Medicine.

As physicians are under pressure to reduce health care spending and find themselves being evaluated in new ways, their incentives have shifted. Many patients are shouldering more of their health care costs through high-deductible health plans, meaning their priorities may not always be aligned. As trust has eroded, those conflicting incentives risk warping the health care encounter in ways that may motivate bad outcomes or cause patients and doctors to consider things other than the best health outcomes.

For example, high-priced cancer drugs come at a time when there is pressure to decrease medical spending. "Physicians are increasingly put into the position of divided loyalty," said Benjamin Djulbegovic, an oncologist at the University of South Florida. "On one hand, we've got to pay attention to costs and the responsible use of societal resources, and on the other hand our loyalty is foremost to individual patients, and we are increasingly taking into account those divided loyalties. I don't think we should put in that position."

Here’s how the prisoner's dilemma is typically posed: Two bank robbers are jailed, and each receives an identical offer: Betray your accomplice by ratting on him, or stay silent. If both robbers stay silent, they both get a lesser charge. If one rats out the other, he'll get out and the other guy will serve time. But if they both betray each other, they both stay behind bars for a long time. The most self-interested choice is to rat out their partner, but two people who act in their own self interest end up each doing something that makes them both worse off.

That may seem like a far cry from the doctor’s office, but in their paper, the research team paints a parallel prisoner's dilemma:

A patient seeking opioids for pain may have real pain or may be faking. If he has real pain, the rational choice for the doctor is to treat him. If he has fake pain, it is still in the doctor’s best interest to treat the patient. Otherwise, the patient will give him a low satisfaction score -- resulting in loss of reputation and reduced income. Thus, a doctor will prescribe opioids regardless of whether the patient needs them, and the patient addicted to opioids will demand these opioids for short-term satisfaction notwithstanding that their long-term use may eventually harm his health and society at large.

In the old days, Ioannidis said, medicine hewed closer to an ideal. Physicians assessed patients' problems and prescribed the best treatments. The revolution underway in the health care system is supposed to cut costs and improve health, but Ioannidis and colleagues are concerned that these may put the interests of patients and doctors in conflict, creating the prisoner's dilemma.

"For a new drug, we need to have experimental evidence, randomized trials, before it’s introduced," Ioannidis said. "For major changes in the health system, which would definitely affect millions and sometimes hundred of millions of people, we just go ahead and do them, and we just take it for granted they should work, because they sound okay."