Everything Everywhere Daily: History, Science, Geography & More - Game Theory

Starting point is 00:00:00 One of the most fascinating areas of mathematics and economics is known as game theory. Game theory involves analyzing competitive situations where multiple participants make independent decisions. In other words, the results will depend not just on what you decide, but what on someone else decides as well. Game theory is applications not just in games, but in business, personal relationships, international diplomacy, and war. Learn more about game theory, and how it applies to different areas of life on this episode of Everything Everywhere Daily. What if your perceptions about the past were wrong? ThruLine is a podcast that takes you back in time to uncover the parts of the story that may have gone unnoticed.

Starting point is 00:00:53 It effectively turned day into night. And how it shaped the world now. Time travel with us every week on the Thurline podcast from NPR. Game theory is on one hand very simple to understand. And on another hand, it can involve very complex mathematics. This episode will just touch on the basics of game theory to give you a better idea of what game theory is and how to think of it in a rational manner like a game theorist. For the purposes of this discussion, a game is any social situation where there are multiple

Starting point is 00:01:29 parties who make strategic decisions, where the outcome is determined by the decisions of the parties involved. So a game is not limited to a game like the type children play, but in this case it can mean literally anything, including negotiation, setting prices, or planning a battle. There can be many different types of games. Cooperative versus non-cooperative, zero-sum versus non-zero-sum, finite versus infinite, symmetric, simultaneous versus sequential, and many others. So let's start with probably the simplest case, a game of Tic-Tac-Tow, or as some of you might know it, knots and crosses.

Starting point is 00:02:06 The first time you ever played it, it was probably when you were a child. It didn't take long to figure out that the outcome of the game didn't just depend on what you did, but also on what your opponent did. It then probably didn't take too long to figure out exactly what your opponent would do, based on what you would do, and that you could play to a draw almost every single time. That's why adults never play tic-tac-toe. But let's take another example, one that's more complex, and is the quintessential example used to demonstrate game theory,

Starting point is 00:02:36 the prisoner's dilemma. In this game, assume that you and your partner in crime robbed a bank and were captured by the police. the police separate you and try to get each of you to implicate the other. Also, assume that you have no particular fondness for your partner and nor do they have any for you. So each of you is looking out for your own self-interest. Now, if you rat out your partner and they stay silent, you will go free and your partner will get 20 years in jail. However, the same is true for your partner. If they implicate you and you stay silent, they go free and you get 20 years in jail.

Starting point is 00:03:11 If you both rat each other out, you will each get five years in jail, and if you both stay silent, you will each spend one year in jail. The first temptation might be to rat out your partner so you can go free. But if your partner is thinking the same thing, then you won't go free. You'll get five years behind bars. Trying to second guess what the other person will do to make your decision will put you into a never-ending loop. What I just described is an example of a finite game.

Starting point is 00:03:40 You play it only once and you play it to win. Likewise, both parties make their choices simultaneously, or at least they do as far as the outcome is concerned as they can't communicate. Under such rules, it's almost impossible to tell what the outcome will be. However, if we change the rules, we can see how the outcome will be different. Suppose the choices were sequential. The police come to you and they tell you the choice your partner already made. At that point, your decision is trivial. You do whatever minimizes your time in jail. Likewise, suppose, that you could communicate with your partner before you each made your decision. In this case, the optimal solution would be for both of you to not talk and each only spend one year in jail.

Starting point is 00:04:19 The optimal strategy for any game will depend on the rules of the game. A game like the Prisoner's Dilemma isn't just a theoretical exercise. There are actual real-world examples. Let's use the examples of Coke and Pepsi. Both Coke and Pepsi would be better off if they didn't have to advertise. They could both save money and increase their profits. However, if one company were to advertise and the other did not, they could gain market share against the other, which would make it in their economic interest to spend money on advertising. The end result is that both companies advertise heavily, if for no other reason, that they don't want to abandon advertising to their competitor.

Starting point is 00:04:57 Perhaps an even better example is that of OPEC. OPEC is a cartel of oil-producing countries. Their members control a significant amount of the world's oil production. If they didn't have a cartel, everyone would have an insolks. to produce as much as possible, which would drop the price. By working together, they can reduce oil production to increase the price. However, the best strategy for any one member of the cartel is to defect from the production quotas. If everyone else in the cartel cuts production to increase the price, one country could keep producing at high levels to take advantage of the price

Starting point is 00:05:31 increase. Every country in the cartel has the same incentives to defect, so in this case it's like a Prisoner's Dilemma with multiple participants. Unlike the classic Prisoner's Dilemma that I outlined, this isn't a game that is played once. It's a game that's played over and over. And moreover, there's communication between all the parties involved. In the case of OPEC, there's actually been many defections from oil production quotas. OPEC doesn't have a lot of teeth to be able to force its members to actually conform to its decisions. However, other cartels, such as medieval trade guilds or labor unions can provide stricter enforcement mechanisms to ensure their members don't defect from production or pricing rules.

Starting point is 00:06:12 There are similar game theory scenarios in sports. For years, the sport of cycling had a problem with performance-enhancing drugs and blood doping. In the late 90s and early 2000s, everyone at the top level of the sport was doing it, and everybody knew that everybody was doing it and that they were getting away with it. As an individual cyclist, what do you do? If you don't cheat, you had no chance of winning. If you did cheat, were you really cheating if everybody else was doing it too? At that point, you weren't cheating for an unfair advantage.

Starting point is 00:06:42 You were just cheating to keep up with everyone else. The study of game theory isn't just about coming up with these scenarios. There is actual mathematics behind it. The systematic development of the theory in game theory was developed by one of the great mathematicians of the 20th century, John von Neumann, and the economist Oscar Morgan Stern. In 1944, they published The Theory of Games in Economic Behavior. They created this branch of mathematics because they felt that the mathematics used in physics and the hard sciences were inadequate to explain the actions of humans who were able to anticipate and react to each other's moves. Game theory was further developed in the 1950s with the work of the mathematician John Nash.

Starting point is 00:07:21 Nash was awarded the Nobel Prize in economics for his work in 1994. And the life of John Nash was also the subject of the movie A Beautiful Mind, starring Russell Crow, which won the Academy Award for Best Motion Pitcher in 2002. Nash's biggest innovation was the development of what is called a Nash equilibrium. A Nash equilibrium is a state in which each player in a game is making the best decision possible, given the decisions of the other players. In other words, no player can improve their own outcome by changing their decision, assuming that all other players' decisions remain unchanged. In the case of the example I gave with Coke and Pepsi,

Starting point is 00:07:56 the Nash equilibrium would be for both companies to continue advertising. In the case of professional cyclists in the early 2000s, the Nash equilibrium was for everyone to use performance-enhancing drugs. A Nash equilibrium doesn't mean it's the best outcome for any particular player or even a good outcome, only that it is the likely outcome. Also, as the name equilibrium would suggest, it's usually something arrived at over time, not with a single action like in the original Prisoner's Dilemma Game. One of the things which spurred game theory research in the second half of the 20th century

Starting point is 00:08:27 was the Cold War. The Cold War can be thought of as a two-player Prisoner's Dilemma game. game. During the Cold War, the United States and the Soviet Union were engaged in a strategic arms race with each side trying to gain an advantage over the other. Each side had to decide whether to cooperate by limiting their arms buildup or to defect by increasing their arms buildup. If both sides cooperated by limiting their arms buildup, they would both benefit by avoiding the costs of an arms race and reducing the risk of nuclear war. However, if one side defected by increasing its arms buildup, it would gain a strategic advantage while the other side suffered a strategic

Starting point is 00:09:03 loss. And this created a strong incentive for both sides to defect, leading to an arms race. I've only given a very simple explanation of game theory and what it is. Game theory is applications in evolutionary biology, business, diplomacy, war, sports, philosophy, computer science, and many other fields. There very well may be aspects of your life where you have to make strategic choices, where the outcome will be influenced by decisions made by one or more other people. And if you find yourself in such a situation, you can probably analyze it through the framework of game theory. The executive producer of Everything Everywhere Daily is Charles Daniel.

Starting point is 00:09:44 The associate producers are Thor Thompson and Peter Bennett. I just want to thank everyone, including the show's producers, who support the show over on Patreon. If you'd like to support the show, just head over to patreon.com, which is currently the only place where you can get show merchandise. Also, if you want to talk to other listeners about the show, head over to our Facebook group or Discord server, both of which have links in the show notes.

Everything Everywhere Daily: History, Science, Geography & More - Game Theory

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