General

What is game theory?

Game theory is a philosophical and psychological theory that attempts to predict the choices that people will make during a “game.” That can refer to actual games like chess or tennis, or events such as military battles and even raising children. Because it’s so helpful to know what people are going to do in a given situation, game theory has wide-reaching implications that have been studied for decades. So, what exactly is game theory, and how does it work?

History of game theory

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Game theory was officially invented in 1944 by mathematician and all-around genius John von Neumann. People had been using game theory long before von Neumann gave it a name, but it was less precise and mathematical. Back in ancient Greek times, Plato had grappled with game theory when thinking about the Battle of Delium and whether or not soldiers would defect.

He imagined a soldier on the front lines waiting to repel an enemy attack. If the defending army successfully repels the attack, chances are likely that the individual soldier wouldn't have had much to do with the defense. If he stuck around, all it would do is increase the likelihood that he would be hurt or killed. If the enemy overwhelms the defense, on the other hand, then it would be even more likely that he would be hurt or killed, so he should run away in this situation, too. No matter the outcome of the battle, it’s beneficial for the soldier to run away.

Application

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Game theory is used for strategic purposes. Once you understand how your opponent is going to react to your actions, you can anticipate their next move and come up with a strategy that will beat that person or team. It can be used in any competitive, or sometimes cooperative, situation. You can use game theory in situations ranging from tic-tac-toe to stock trading to major military battles.

Chances are you’ve used game theory quite a bit. When you’re playing rock-paper-scissors with your friend, game theory is that little voice in your head that says, “She picked rock last time, so she probably won’t pick it again. It should be safe to use scissors.” You’re anticipating your opponent’s next move and using the previous information to craft your strategy. Game theory just takes it one step further and applies mathematical and psychological formulas to make more informed decisions.

What counts as a game?

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The “games” used in game theory have to be events in which the opponents can actively compete against one another. Opponents don’t necessarily have to be people, but they do have to resist the advances of the other.

For example, a lumberjack cutting down a tree doesn’t work for game theory. The tree won’t fight back, and the lumberjack can use basic statistics for the best way to chop the tree down. The coach of a football game, however, has to use game theory, because his opponent will actively try to counter any efforts made to score. He needs to think about what the opponent might do and use that information to win.

Classifications of games

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Games can be broken into several categories. They are first categorized based on the number of players. There are one-person games, two-person games, and games with more than two players.

They can then be categorized into games of perfect information or imperfect information. Chess is a game of perfect information because both players have all the information about what’s going on. Poker is a game of imperfect information since none of the players know what cards are in their opponents’ hands.

Finally, there are constant-sum or variable-sum games. Competitors in a constant-sum game are in total conflict. One person or team wins, and the others lose. Poker and chess are both constant-sum games. In a variable-sum game there can be multiple winners or losers. This could be a labor dispute between a company and its employees. In the end, both parties want to win and come to an agreement, but during the negotiations, they are at odds against one another. Variable-sum games can also be cooperative or non-cooperative. A labor dispute would be characterized as cooperative because both parties are working together to reach an agreement. Bidding at an auction would be considered non-cooperative because everyone is bidding independently.

Example of game theory

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For you thinkers out there, here’s a fun game theory brain teaser for you. Imagine that you’re trying to cross a rough river that you can’t swim or take a boat across. There are three bridges that can get you to the other side. Bridge number one is completely safe and free of obstacles, bridge two has large rocks above it that have a 10% chance of falling, and bridge three is full of venomous snakes that have a 20% chance of biting you. Choosing a bridge at this point isn’t game theory, since there’s no opponent. It’s just a statistical choice.

Now, imagine that you’re a fugitive and there’s a detective on the other side waiting to take you to jail. This complicates things. Now you have to decide not only which bridge is the safest for you to take but also which bridge the detective would least expect you to take. Would he be waiting at the end of bridge one because it’s the safest, or, knowing that you’d think that, would he be waiting after bridge two because it’s the second safest route? Which bridge do you take? That’s game theory.