One of the most fascinating areas of mathematics and economics is game theory.
Game theory involves analyzing competitive situations where multiple participants make interdependent decisions. In other words, the result will depend not just on what you decide but on what someone else decides as well.
Game theory has 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.
Game theory is, on one hand, very simple to understand, and on the other 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 in a rational manner like a game theorist.
For the purposes of this discussion, a game is any social situation where there are multiple parties who make strategic decisions, where the outcome is determined by the decisions of the parties involved.
A game is not limited to a game like the type children play, but in this case, it can mean anything, including things like negotiations, setting prices, or planning a battle.
There can be many different types of games. Cooperative vs. non-cooperative, zero-sum vs. non-zero-sum, finite vs. infinite, symmetric vs. asymmetric, simultaneous vs. sequential, and many others.
Let’s start with probably the easiest case, a game of tic-tac-toe, or as some of you might know it, naughts and crosses.
The first time you played 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 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 every single time.
That is why adults never play tic-tac-toe.
Let’s take another example that is more complex and is the quintessential example used to demonstrate game theory: 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.
You have no particular fondness for your partner, nor do they have any for you, so each of you is looking out for your own self-interest.
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.
If you both rat out each other, you each get five years in jail, and if you each 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. You play it only once. Likewise, both parties make their choices simultaneously, or they do at least as far as the outcome is concerned, as they can’t communicate.
Under such rules, it is 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 that your partner made. At that point, your decision is trivial. You just 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 not to talk and for each to take one year in jail.
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 exorcise. There are real-world examples.
Let’s use the example 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 is that they don’t want to abandon advertising to their competitor.
Perhaps an even better example is 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 incentive 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 of the members 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 increase.
Every country in the cartel has the same incentives to defect, so in this case, it is 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 is a game played over and over. Moreover, there is communication between all the parties involved.
In the case of OPEC, there have 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 and labor unions, can provide stricter enforcement mechanisms to ensure their members don’t defect from production or pricing rules.
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 everyone knew that everyone else 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 everyone else was doing it too? At that point, you weren’t cheating for an unfair advantage. 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 greatest mathematicians of the 20th century, John von Neumann, and the economist Oskar Morgenstern.
In 1944 they published The Theory of Games and Economic Behavior. They created the theory because they felt that the mathematics used in physics and the hard sciences were inadequate to explain the action 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 mathematician John Nash. Nash was awarded the Nobel Prize in Economics for his work in 1994. The life of John Nash was also the subject of the movie A Beautiful Mind starring Russel Crowe, which won the Academy Award for Best Motion Picture 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 all other players’ decisions remain unchanged.
In the case of the example I gave with Coke and Pepsi, 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 is 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 is 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 was the Cold War.
The Cold War can be thought of as a two-player prisoner’s dilemma.
During the Cold War, the United States and the Soviet Union were engaged in a strategic arms race in which each side was trying to gain an advantage over the other.
Each side had to decide whether to cooperate by limiting their arms buildup or 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 loss. This created a strong incentive for both sides to defect, leading to an arms race.
I have only provided a very simple explanation of game theory and what it is. Game theory has applications in evolutionary biology, business, diplomacy, war, sports, philosophy, computer science, and many other fields.
There may very well 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. If you find yourself in such a situation, you can probably analyze it through the framework of game theory.