John Nash: It’s All About the Game
Picture this:
You’re on a game show where you face off with another contestant in deciding whether you should split or steal a hefty pot of money. Each player is given the two options and must choose in secret of their intentions. If both choose to split, they each receive half of the pot. If one chooses to steal and the other chooses to split, the one who chooses steal takes the whole pot. If both choose to steal, neither player takes home any money.
Great game idea, right? Well, there is actually a show called “Golden Balls” that has this scenario right at the very end. Check out it out.
The reason behind this preface is that it is based on John Nash’s Nobel Prize-winning contribution to economics.
The Game Master, Mr. John Nash
John Nash was one of three winners of the Nobel Prize in Economics in 1994 “for their pioneering analysis of equilibria in the theory of non-cooperative games.” Basically, John Nash was responsible for popularizing the sub field of economics known as “game theory.” Not only was his contribution turned into a game show, his story is told in the critically acclaimed movie A Beautiful Mind, where he is portrayed by Russell Crowe. In the movie, naturally, Nash’s “aha!” moment happens at a bar, where five women come into the bar and there are only four guys, including him. However, this famous bar scene is often criticized as not accurately depicting his theory. For those in the know, comment below and share where they went wrong.
People make decisions, based on their own preferences, that will make them better off. When two people, with different preferences, are making simultaneous decisions, like in the final round of Golden Balls, the outcomes often deviate from what the decision makers had in mind. The analysis of this phenomena is game theory.
The Prisoner’s Dilemma
Imagine that my fellow blogger Alex and I get arrested for allegedly pulling off one of the greatest heists of the 21st Century. So, they have Alex and I locked up in separate rooms and the investigators offer us a deal if we confess. Here is how this game shakes out.
Which route would result in both Alex and I serving the least amount of time? If we both were to lie, the police would not be able to stick too much onto either of us, and we would each serve only one year in prison. We didn’t plan on getting caught so we didn’t plan out what we should do in this case. We also can’t talk to each other or collude. If I confess when Alex chooses to lie, I get off scot-free and Alex has to serve a whopping ten years in prison. If Alex confesses and I lie, then I’m screwed. Sorry, but there’s no way I’m risking those stakes for Alex. I like Alex, but not that much and honestly, I don’t think I’m worth that risk to Alex either. So, we both end up confessing and getting eight years in the slammer. This type of game is called the Prisoner’s Dilemma. What ended up happening is that we deviated away from the best outcome for us (Lie, Lie) to a less optimal equilibrium (Confess, Confess).
How Do We Fix this?
One way you solve this dilemma is through the use of repetition and enforcement mechanisms. Now imagine we are crappy criminals and try to rob convenience stores regularly. We’ve agreed beforehand to both lie if we are ever caught. The first couple times, we lie and get out with a tiny sentence. But, on one occasion, Alex ticks me off and I confess when we’re brought in. The next time — assuming Alex is dull enough to continue robbing convenience stores when he gets out — Alex will punish me for violating that agreement and I would end up getting the full punishment. Eventually, if we keep repeating this game enough times, we come back to the equilibrium where we both lie and get the tiny sentences.
Other Uses Of Game Theory
Since the time of John Nash, game theory has been used in a variety of fields. For example, it has been used to analyze business decisions. Should a business enter a market? Will their competitors lower their price and pull away all the customers? Should a business spend money on advertising? Game theory is used in football. It was used to support the extremely unpopular play call of the Seattle Seahawks during Superbowl 48, when they called a passing play on second and goal from the one yard line — yeah, it still stings. Politics is also laden with game theory as it is used to determine what routes a political opponent might take in their path to election.
What is the Equilibrium?
There are many different venues for explaining the choices consumers, politicians and business’ alike make. John Nash used mathematics to explain the payoffs associated with choices as a way of explaining their actions. His research was insightful in giving economists an extra tool set and lens from which to analyze human action. If you ever end up on that show with a pretty girl, learn from that poor man’s mistake, don’t trust her!
