Game theory
The beginning of the Game theory began in 1944, when the book called The Game Theory and Economic Behavior by John von Neumann and Oskar Morgenstern was written.
Game theory is a branch of, originally, applied mathematics, used mostly in economics and political science, a little bit in biology, that gives us a mathematical taxonomy of social life and it predicts what people are likely to do and believe others will do in cases where everyone's actions affect everyone else. That's a lot of things: competition, cooperation, bargaining, games like hide-and-seek, and poker. [1]
Games in Extensive Form
All the games that we are considering in this chapter have certain things in common and these are:
- There is finite set of players (who may be people, groups of people holding the same opinion, or more abstract entities like computer programs or “nature” or “the house”).
- Each player has complete knowledge of the rules of the game.
- At different points in the game, each player has a range of choices or moves. This set of choices is finite.
- The game ends after a finite number of moves.
- After the game ends, each player receives a numerical payoff. This number may be negative, in which case it is interpreted as a loss of the absolute value of the number. For example, in a game like chess the payoff for winning might be +1, for losing -1, and for a draw 0.
In addition, the following are properties which a game may or may not have:
- There may be chance moves. In a card game, the dealing of the hands is such a chance move. In chess there are no chance moves.
- In some games, each player knows, at every point in the game the entire previous history of the game. This is true of tic-tac-toe and backgammon but not of bridge (because the cards dealt to the other players are hidden). A game with this property is said to be of perfect information. Note that a game of perfect information may have chance moves. Backgammon is an example of this because a die is rolled at points in the game.
It has been just said that the players receive a numerical payoff at the end of the game. In real conflict situations, the payoff is often something nonquantitative like "happiness", "satisfaction", "prestige", or their opposites. In order to study games with such psychological payoffs, it is first necessary to replace these payoffs with numerical ones.
- A week in Paris.
- A week in Hawaii.
- Eight hours in a dentist‘s chair.
Different people would assign different “happiness ratings” to these prizes. For a person with an interest in French culture, rating them as 100, 25, -100, respectively, might be reasonable. To a surfer, the ratings might be 10, 100, -100. The point is that we are assuming that this conversion of nonquantitative payoffs to numerical ones can always be done in a sensible manner.[2]
