Game theory is a branch of mathematics that studies strategic decision making in situations where multiple individuals or entities interact. In other words, it is a study of rational behavior in a social context. While game theory has its roots in economics, it has become increasingly relevant in fields such as politics, biology, psychology, and computer science. This article will explore the basics of game theory, its applications, and its criticisms, as well as how it can be applied to everyday decision making.
Plato, in two of his texts, "The Laches" and "The Symposium," explains how Socrates recalls an episode from the famous Battle of Delium in 424 BC between the Athenians and the Boeotians. The synopsis of this passage goes as follows: consider a soldier at the front of the battling line having the following realization: if our defense is successful, I still risk the chance of dying; if our defense is unsuccessful, I will almost certainly die. Based on this reasoning, it seems that the best alternative for the soldier is to run away, regardless of who is going to win the battle. Now, imagine if all soldiers were to exhibit this very reasoning at the same time. If such an event would occur, they would all probably realize that they would be better off running away. The seemingly simple yet incredibly reasonable hypothesis is one of the first historical instances of game theory.
Flash forward 2,368 years to 1944, when Hungarian-American mathematician John von Neumann published a book titled "Theory of Games and Economic Behavior." This foundational work contains the method for finding mutually consistent solutions for two-person zero-sum games. This great book introduced game theory as a concept, thus extending its application to fields like economics, politics, and sports and leading to the expansion of the array of scientists that showed interest in it. One of those scientists was the legendary John Nash, who won the Nobel Memorial Prize in Economic Sciences in 1994 and popularized the idea of game theory as we know it today.
What is a game?
Something fundamental about game theory is that it doesn't get its name from the preconceived notion of a game as we understand it. A game in game theory is an interaction between multiple people in which each player's payoff is affected by the decisions of others. Namely, any single interaction you're part of can be analyzed with game theory in order to produce the most beneficial outcome. But before we get into the mechanics, let's lay out the main principles:
- A game needs to include multiple players.
- The players need to interact with each other.
- There needs to be a reward.
- We assume that players act rationally.
- We assume that players act according to their personal self-interest.
Prisoner's dilemma
The prisoner's dilemma is the most widely mentioned game in game theory. The basic premise is how to establish a mutually beneficial strategy between two members of a gang that got arrested and face potentially imprisonment. The rules are as follows:
- The players of the game are Prisoner A and Prisoner B.
- The players can't communicate with each other.
- If A and B each betray each other, each of them serves two years in prison.
- If A betrays B, but B remains silent, A will be set free, and B will serve three years in prison, and vice versa.
- If A and B both remain silent, both of them will only serve one year in prison.
This matrix depicts the different choices of each member and signifies the number of years to serve. According to the prisoner's dilemma, it exemplifies to a great degree the substrate of human nature. The irrational self-interest-driven gang member will most probably choose to betray his counterpart, thinking that he will get a better deal. This idiosyncratic choice will most certainly lead to a disaster for both parties since they will get the worst deal possible. The obvious mutually beneficial choice here is to keep silent.
The main idea behind this game is to expose the inherent tendency of humans to display a lack of cooperation in decent, similar games. Game theorists usually coined the terms dominant strategy and Nash equilibrium to distinguish the kind of strategies followed by the players. Those two terms are usually used together and form the basis upon which game theory is founded.
Dominant strategy refers to strategies that are better than other strategies for one player no matter how the opponent may play. Those strategies might be great in the case of non-alternatives. But if you're part of a game with more dominant strategies, which means its player has his own dominant strategy, then they aren't optimal. In the prisoner's dilemma case, the dominant strategy for each player is to betray, and here is where the term Nash equilibrium comes into play.
The term is used since John Nash explained the essentiality of equilibrium in his landmark work "Equilibrium points in N-person games." In essence, what he proposed is that even high-level competitive games like Google vs. Apple or USA vs. Russia, there exists an equilibrium where no side would benefit by changing its course. At this equilibrium, each side knows its adversary very well and sticks to its strategy. For instance, in the prisoner's dilemma, the Nash equilibrium is the upper left square of the matrix, which means both prisoners need to stay silent.
What makes Nash's theory of equilibrium so special is that it presupposes that in each game, there is at least one point of equilibrium, and all players will be better off trying to find it and form their strategy around it. This momentous revelation helped people in disciplines like politics, war, economics, business, and social theory understand the world better and form better strategies.
Even if people or companies rationally follow their self-interest, the best outcome is hard to reach when they can't or don't cooperate. Therefore, the best strategy is to continually scan the market for potential alliances. People who can forge strong alliances will eventually become part of oligopolies and thus dominate their market. The rest will consequently be ostracized.
That's what I love about game theory. It approaches the game of life from its most axiomatic principle - that of evolution. Evolution equals adaptation and therefore, life is an omnipresent game of adaptation. Humans thrive in cooperation because it is the main strategy that helped us survive and thrive after years of adversity and struggle to compete against different forces of nature. The sad thing is that after establishing our sovereignty, we overpowered other species and in most occasions, nature itself. But eventually, we turned ourselves against each other.
There are a variety of factors that affect the descent to the point we have reached, but a game theory mindset can work to our advantage. I always believed that change and equilibrium start at the micro-level, and that is something we fail to grasp because we are usually consumed by events at the macro. It is interesting to be in the know and discuss and argue about politics and national strategies, but at the end of the day, the trigger is pulled by the respective strategists.
Game theory can explain humanity’s biggest problem
During a discussion on the ideals of the Enlightenment, it is mentioned that the concept of using knowledge to improve human well-being is not a natural one. For most of our history, there was no knowledge that could be acted on to reduce infection, tribal warfare, or extend life. Until recently, it would have been unrealistic to even hope for such things. Despite this, we should endorse and advance enlightenment humanism and remind ourselves of what is great about it, as there is always a tendency towards backsliding.
For instance, scientific findings, the efficacy of vaccines, and the reality of climate change have been blown off, and enlightenment values have been ignored in the war in Ukraine. For Putin, the lives of hundreds of thousands of people dying and their infrastructure being reduced to rubble are a small price to pay for the glory and avenging of the Soviet Union's humiliation. However, even though we are not wired for enlightenment humanism, we ought to endorse it and strive towards it.
One idea that is essential in understanding our current predicament comes from 'game theory.' Game theory is concerned with what is the rational thing to do when the outcome depends on what other rational people do. The 'Tragedy of the Commons' is a game-theoretical predicament where what everyone does that is rational for them leaves everyone worse off when everyone does it. Many situations confront us where tragedies of the commons are present, such as when waiting for the bus in the rain instead of driving an SUV. If everyone thinks that way, we are all in danger of being cooked.
Another arena in which we have a tragedy of the commons is rationality itself. Suppose a person thinks, "Should I believe this, or should I believe that?" If I believe this, I will be a hero in all the people that matter to me. Another member of the group thinks that and another member, and they all think, "Well, if you doubt that, then you're making us look kind of stupid and evil." If everyone believes that, then you can have two sides, each of which is individually rational, but the whole society is worse off because you have warring tribes instead of a joint search for the truth. In this case, the commitment to truth is more important than a slogan that makes your side look good in order for everyone to enjoy what is objectively good for everyone.
Despite the threats from the identitarian left, populist right, nationalist leaders, and religious fundamentalists, there is still hope. Civilization, in general, tends to slowly drift in the direction of greater rationality. Science knows more than it did 50 or 100 years ago, and many superstitious beliefs have been marginalized. Progress has been made not only in factual beliefs but also in moral beliefs such as slavery, disenfranchising women, criminalizing homosexuality, and segregation of schools. We have come a long way, and humanistic values have a kind of built-in advantage because they appeal to our common humanity.
Despite our differences in race, religion, ethnicity, and nationality, we all want to be alive, healthy, and educated. Enlightenment humanism is just appealing to that common humanity, even though it is not particularly intuitive. We should continue to advance it and remind ourselves of what is so great about it.
What each of us could do instead is to use game theory in our most challenging decisions in our closest relationships. Regardless of what decision you have made and how this will impact your future, think like a game theorist. Ponder questions like, are the actors in the situation rational? Are we able to reach Nash equilibrium? Do they act according to their self-interest? Do they understand the rules of the game? Is their dominant strategy really that dominant?
If you see that most game theory parameters aren't met, you know that you have to change your approach. You either need to also act rationally, which is something I wouldn't suggest, or you need to step away and find better players or games. The choice is always yours. Life often feels like a game, and usually, the winners are those who know how to play."
See more: How science is taking the luck out of gambling, The game you win by losing (Parrondo's Paradox)
FAQ
Q: What is Game Theory?
A: Game Theory is a branch of mathematics that studies decision-making in situations where two or more individuals are interacting with each other. It provides a framework for understanding how people make choices and how these choices affect outcomes.
Q: Why is Game Theory important?
A: Game Theory is important because it helps us understand how people make decisions in strategic situations. It provides insight into how people behave in different types of situations, such as negotiations, conflict, and cooperation.
Q: How can I use Game Theory in my daily life?
A: You can use Game Theory in your daily life by applying its principles to decision-making. For example, you can use it to evaluate potential outcomes and choose the best course of action in situations such as job interviews, negotiations, or personal relationships.
Q: Can Game Theory be applied to business?
A: Yes, Game Theory is widely used in business and economics. It can be used to model and analyze various strategic interactions, such as pricing, advertising, and competition between firms.
Q: Is Game Theory applicable to social sciences?
A: Yes, Game Theory is applicable to social sciences such as sociology, political science, and psychology. It can be used to model and analyze various types of social interactions, such as voting behavior, cooperation, and conflict resolution.
Q: What are the limitations of Game Theory?
A: Game Theory has some limitations. It assumes that individuals are rational and always act in their best interest, which may not be true in all cases. It also assumes complete information, which is often not the case in real-world situations.
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