Our world is immersed in game theory! Walk to your nearest video store and perhaps stumble across The Dark Knight, whose ending ferry scene exhibits a scenario close to the Prisoner’s Dilemma. Turn on the television, and you might see the Weakest Link or Survivor, both of which are sequential-form games. History too has seen links to game theory; the Cuban Missile Crisis was really a game of chicken.
You might have heard of game theory from A Beautiful Mind, a movie about game theory mathematician, John Nash. His work is interesting, not only because most was done when he was diagnosed as a paranoid schizophrenic, but because it won him a Nobel Prize in Economics. A mathematician winning a Nobel Prize you say? Yes, its possible!
Rumor has it that Alfred Nobel, founder of the awards, did not include an award for mathematics because of his jealousy over his wife’s affair with a mathematician. Whatever the reason, for a mathematician to win a Nobel Prize is a rare and phenomenal incident. To win it for work in game theory really states about the topic: game theory is exceptionally important in the field of economics.
What is game theory?
Game theory is a branch of mathematics that studies individual decisions and their outcomes. Compared to other areas, game theory is relatively new, as it only started to be extensively studied during the 20th century. The progress made in the area is great however and now, game theory has been applied to everything from biology to political science. For those of you taking AP Microeconomics, you’ll know that game theory has major applications in business.
What is a game?
The fundamental building block of game theory is a scenario game theorists call a game. Though it is quite different from the traditional games you would might play in your living room, these game theory games have some similar characteristics.
1) Every game has players.
A tree can be a player. So can your Uncle Joe! These players can be just about anything, from individuals to groups, investors to corporations, governments to even nature! Players are just those who participate in the game.
2) Each player has a decision and its outcome
Like joysticks and buttons on an Xbox controller, each player can make its own decision to create a desired effect in the” game”. Not only that, but their decisions can and usually will affect other players’ decisions and outcomes as well.
3) Each player usually wants to “win”
Pick any game off of a shelf and it is likely to always have an objective. In game theory, the objective for all players is the same: to win. “Winning” is not usually the same as the way we usually define it. Though in ordinary games, we think of winning as “beating everyone else”, in game theory games it is not necessarily so! Instead, every player tries to “win” by, what mathematicians call, maximizing their utility. We’ll discuss this in a subsequent article.
There you have it! Game theory is a simple, yet powerful branch of mathematics that is easy to learn and hard to forget. There’s a reason why countless papers on game theory are submitted to research fairs every year. Sooner or later, you’ll start seeing everyday areas of life where game theory is being applied!
Stay tuned for more…