Game Theory in Prison and Hospitals
The prisoner’s dilemma is a well-known situation that is often depicted in television shows such as Prison Break, Orange is the New Black, Castle, and White Collar. As was discussed in class, it occurs when two connected convicts are detained in separate prison cells, each given the option of either staying silent or confessing to their crimes and getting immunity while their partner is imprisoned for life. If both were to confess, then both would be sent to jail, but if both were to remain silent, then both would potentially face minimal charges. The best solution for the two would be if the they could somehow communicate and trust one another to not take the immunity deal. However, the only Nash equilibrium solution to this dilemma is for both to confess. With time, each player also becomes wiser and tends to choose the options predicted by the Nash-equilibrium solution (in this case, both confessing). Experiments showed that by the tenth round, only about 10% of the convicts were still choosing to remain quiet.
This prisoner’s dilemma shows that what is best for an individual can be the worst option for the entire group, and oftentimes in the real world, the worst option is what occurs. Another example that also leads to this conclusion can be seen in employees competing with one another to show more “face time” at the office in order to impress their bosses. The result is “workforce exhaustion” as more and more people get in earlier and stay later at work.
Examples can also be seen throughout history. In the 1940’s, hospitals were competing with one another to hire the top medical students. However, due to the ongoing World War II at the time, there was a scarcity of top students, and as a result, hospitals sent out offers to candidates earlier and earlier each year. Ultimately, this was the worst possible outcome for all involved parties. Hospitals were hiring students before the candidates had even passed all of their exams and students had less time to decide between offers. Nowadays, in order to solve this problem, there is a new system in place for matching students to hospitals. Candidates initially submit their top choices for hospitals and are assigned to one based off of mutual preference. No student can change their preferences after submitting them and no hospital can go around this system to hire a better candidate.
Over the years, the Nash equilibrium has changed in order to better fit real-world situations. There have been many examples in which there were multiple possible Nash equilibria. Additionally, analysis on situations must now include the factoring in of non-credible threats (like a child threatening to run away from home if his phone is taken away). Finally, even with these changes, the Nash equilibrium cannot always correctly predict results. It only works if both opponents understand what the other wants and if both make their decisions using rational thought. Otherwise, there would be discrepancies between the actual outcome and the prediction.
Source: https://www.economist.com/news/economics-brief/21705308-fifth-our-series-seminal-economic-ideas-looks-nash-equilibrium-prison