An Introduction to Game Theory
In short, game theory is the study of strategic interaction. This means that how well you do depends on the actions of others as well as your own choices. Games are a common showcase of strategic interaction; games like chess or Connect 4 are played between two different players, and the actions of one player are dependent on the other's.
The concept of rationality is essential to understanding game theory. Rationality refers to players understanding the setup of a game, and being able to reason out the right moves to play. Game theory only works with rationality; in order to make my decision, I would have to assume that my opponent is rational and knows what they're doing. At the same time, I would have to also know that my opponent knows what I'm doing. And vice versa.
Thaler's guessing game is a good example of rationality, in which contestants must pick a number between 0 and 100. The winner is the one with the number closest to two-thirds of the average of all numbers entered in the contest. Without rationality, we would assume other contestants wouldn't know how to play, which would mean their guesses would be random. This would make the average 50, and thus the best guess would be 33. But we assume they are rational, and we would think one level higher, choosing 2/3 of this "best" guess - 22. Yet we could also assume that everyone else knows that everybody is rational, making 2/3 of 22, or 15, the best answer. And so on.
Game theory can be seen almost everywhere in real life. The financial market, for example, is one of the largest applications of game theory. Based on rationality, we try to predict the prices of stocks, hoping to sell at a higher price and win in a net zero sum game. It's the reason why we have bubbles, or excessively inflated prices.
As we head off to college, we will soon witness game theory as we live with dormmates. Chores are shared between two dormies, and each person can either do the chores or not do the chores. Creating a payoff matrix (2 by 2 table showing the "profits" for each person), we can arbitrarily set up some profit values for each outcome. If dormie A and B both do the chores, they both profit with a value of 10. If neither clean up, they both profit only with a value of 2. If A cleans up but B doesn't, A does not profit but B profits by 20. And vice versa. Using the Nash equilibrium, we see that there's a problem: if either dormie expects the other not to clean up, then their response is to not do the chores either. This would make the Nash equilibrium {do not do the chores, do not do the chores}.
Some other examples...in political science, a candidate's platform acts based on the announcements of their rival's. In computer science, networked computers compete for bandwidth. In economics, businesses compete based on the actions of competitors.
Winning number to Thaler's guessing game: 13
Sources:http://www.ams.org/publicoutreach/feature-column/fcarc-rationality
https://www.ft.com/content/6149527a-25b8-11e5-bd83-71cb60e8f08c
The concept of rationality is essential to understanding game theory. Rationality refers to players understanding the setup of a game, and being able to reason out the right moves to play. Game theory only works with rationality; in order to make my decision, I would have to assume that my opponent is rational and knows what they're doing. At the same time, I would have to also know that my opponent knows what I'm doing. And vice versa.
Thaler's guessing game is a good example of rationality, in which contestants must pick a number between 0 and 100. The winner is the one with the number closest to two-thirds of the average of all numbers entered in the contest. Without rationality, we would assume other contestants wouldn't know how to play, which would mean their guesses would be random. This would make the average 50, and thus the best guess would be 33. But we assume they are rational, and we would think one level higher, choosing 2/3 of this "best" guess - 22. Yet we could also assume that everyone else knows that everybody is rational, making 2/3 of 22, or 15, the best answer. And so on.
Game theory can be seen almost everywhere in real life. The financial market, for example, is one of the largest applications of game theory. Based on rationality, we try to predict the prices of stocks, hoping to sell at a higher price and win in a net zero sum game. It's the reason why we have bubbles, or excessively inflated prices.
As we head off to college, we will soon witness game theory as we live with dormmates. Chores are shared between two dormies, and each person can either do the chores or not do the chores. Creating a payoff matrix (2 by 2 table showing the "profits" for each person), we can arbitrarily set up some profit values for each outcome. If dormie A and B both do the chores, they both profit with a value of 10. If neither clean up, they both profit only with a value of 2. If A cleans up but B doesn't, A does not profit but B profits by 20. And vice versa. Using the Nash equilibrium, we see that there's a problem: if either dormie expects the other not to clean up, then their response is to not do the chores either. This would make the Nash equilibrium {do not do the chores, do not do the chores}.
Some other examples...in political science, a candidate's platform acts based on the announcements of their rival's. In computer science, networked computers compete for bandwidth. In economics, businesses compete based on the actions of competitors.
Winning number to Thaler's guessing game: 13
Sources:http://www.ams.org/publicoutreach/feature-column/fcarc-rationality
https://www.ft.com/content/6149527a-25b8-11e5-bd83-71cb60e8f08c
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