Game theory as a formal mathematical framework was invented in the early 20th century by mathematicians such as Émile Borel, John von Neumann, and Oskar Morgenstern. However, the roots of game theory can be traced back to ancient civilizations such as ancient Greece, where philosophers such as Plato and Aristotle discussed the concept of strategic decision-making.
The formal development of game theory was motivated by a desire to model and analyze strategic interactions in economics and other social sciences. In the early 20th century, economists were interested in understanding the behavior of firms in oligopolistic markets, where a few large firms dominate the industry. Game theory provided a framework for modeling the strategic decisions made by firms in such markets and predicting the outcomes of their interactions.
Over time, game theory has been applied to a wide range of fields, including political science, biology, psychology, and even computer science. Today, game theory continues to be an important tool for modeling and analyzing strategic decision-making in many different contexts.
So what is it in simpler, terms?
Imagine a small village with many farmers who all own goats. Every summer, they all bring their goats to graze on the village green. But the green can only support a limited number of goats, beyond which adding more goats will harm the rest.
Each farmer wants to own as many goats as possible, because each goat brings them some profit. However, they also have to consider the well-being of the goats and the other farmers. If too many goats are grazing on the green, they will all suffer and no one will benefit.
So the farmers must make a decision: how many goats should each of them own? If one farmer owns too many goats, they will harm the others and ultimately harm themselves. But if everyone owns too few goats, they will all miss out on potential profit.
Game theory can help us analyze this situation by modeling it as a game. Each farmer must choose how many goats to own, and their payoff depends on the number of goats owned by themselves and the other farmers. The goal is to find a “Nash equilibrium”, where no farmer can improve their payoff by unilaterally changing their strategy.
This situation is similar to many real-world scenarios, where individuals or companies must balance their own interests with the interests of others. Game theory can help us understand how people make decisions in these situations and find optimal outcomes that benefit everyone involved.
Game theory is like playing a game of chess. When you play chess, you have to think about what moves your opponent might make and how you can counter them. You have to plan your moves ahead of time and try to outsmart your opponent.
In the same way, game theory is about thinking ahead and making decisions based on what other people might do. For example, if you and your friend are trying to decide what movie to watch, you might suggest a movie that you think your friend will like, even if it’s not your favorite. This is because you want to make your friend happy and you know that if your friend enjoys the movie, they might be more likely to pick a movie that you like next time.
Game theory is all about thinking about how your actions will affect other people’s actions and trying to make the best decision based on what you think they might do.
During the Cold War, the concept of Mutually Assured Destruction (MAD) was a prominent example of game theory in the context of nuclear war. The idea behind MAD was that if two countries possessed nuclear weapons, and each knew that the other had the ability to retaliate with equal force, then neither would be willing to initiate a nuclear attack. The fear of retaliation would act as a deterrent, preventing either country from launching an attack.
MAD can be seen as a form of game theory because it involves two parties making decisions based on what they think the other party might do. Each country had to consider the possible outcomes of their actions, and weigh the potential benefits of a nuclear attack against the certain costs of retaliation. By understanding the logic behind their opponent’s decisions, each country could try to manipulate the situation in their favor.
The Prisoners’ Dilemma is a classic example in game theory that can help us understand how two individuals might make decisions when faced with the same situation. In this scenario, two suspects are arrested and charged with a crime. Each suspect is held in a separate cell and has no way of communicating with the other. The police offer each suspect a deal: if one confesses and the other does not, the confessor will get a reduced sentence, while the non-confessor will receive a much harsher punishment. If both confess, they will both receive a moderate sentence. If neither confesses, the police will have to release them due to a lack of evidence.
Game theory can help us understand how the suspects might make decisions in this scenario. Each suspect has two options: to confess or not to confess. The outcome of their decision depends on what the other suspect does. If both suspects stay silent, they both go free. However, if one confesses and the other does not, the confessor gets a reduced sentence, while the non-confessor gets a much harsher sentence. If both confess, they both receive a moderate sentence.
Game theory can help us analyze this situation by creating a matrix that shows the payoffs for each combination of choices. If both suspects confess, they both receive a moderate sentence. If one confesses and the other does not, the confessor gets a reduced sentence, while the non-confessor receives a much harsher sentence. If both stay silent, they both go free. By analyzing the payoffs, we can see that each suspect has an incentive to confess, regardless of what the other suspect does. This creates a dilemma, where both suspects would be better off if they both stayed silent, but each has an individual incentive to confess.
Game theory can be applied to many different fields, including creative endeavors such as art, music, and design. One way to use game theory in creative endeavors is to analyze the decisions made by artists, musicians, or designers and how they are influenced by the preferences of their audience or other stakeholders.
For example, a musician might use game theory to determine the best setlist for a concert, taking into account the preferences of the audience and the optimal balance between new and familiar songs. A visual artist might use game theory to decide how to allocate their time between creating new work and promoting their existing work. A graphic designer might use game theory to design a logo that will appeal to both the client and their target audience.
Another way to use game theory in creative endeavors is to incorporate game elements into the creative process itself. This can be seen in various forms of interactive art, where the viewer’s choices or actions affect the outcome of the artwork. Game elements can also be used in collaborative projects, where multiple participants must work together to achieve a shared goal.
Game theory can be a useful tool for game designers. By analyzing the strategic decisions that players make, designers can create more engaging and rewarding gameplay experiences. Game theory can help designers balance gameplay mechanics, encourage player cooperation, balance risk and reward, and create interesting and meaningful choices for players.
For example, game theory can be used to create balanced gameplay where no player has an unfair advantage. Game theory can also help designers encourage cooperative play and prevent harmful or unproductive behavior. Additionally, game theory can be used to balance the risks and rewards of different actions in the game and create interesting and meaningful choices for players.