## Game Theory: Basic Concepts

Introduction
The Terminology
Basic Concepts of Game Theory
Types of Games
Applications of Game Theory
A Simple Example

Game
A conflict in interest among n individuals or groups (players). There exists a set of rules that define the terms of exchange of information and pieces, the conditions under which the game begins, and the possible legal exchanges in particular conditions. The entirety of the game is defined by all the moves to that point, leading to an outcome.

Move
The way in which the game progresses between states through exchange of information and pieces. Moves are defined by the rules of the game and can be made in either alternating fashion, occur simultaneously for all players, or continuously for a single player until he reaches a certain state or declines to move further. Moves may be choice or by chance. For example, choosing a card from a deck or rolling a die is a chance move with known probabilities. On the other hand, asking for cards in blackjack is a choice move.

Information
A state of perfect information is when all moves are known to all players in a game. Games without chance elements like chess are games of perfect information, while games with chance involved like blackjack are games of imperfect information.

Strategy
A strategy is the set of best choices for a player for an entire game. It is an overlying plan that cannot be upset by occurrences in the game itself.
Payoff
The payoff or outcome is the state of the game at it's conclusion. In games such as chess, payoff is defined as win or a loss. In other situations the payoff may be material (i.e. money) or a ranking as in a game with many players.

Extensive and Normal Form
Games can be characterized as extensive or normal. A in extensive form game is characterized by a rules that dictate all possible moves in a state. It may indicate which player can move at which times, the payoffs of each chance determination, and the conditions of the final payoffs of the game to each player. Each player can be said to have a set of preferred moves based on eventual goals and the attempt to gain a the maximum payoff, and the extensive form of a game lists all such preference patterns for all players. Games involving some level of determination are examples of extensive form games.

The normal form of a game is a game where computations can be carried out completely. This stems from the fact that even the simplest extensive form game has an enormous number of strategies, making preference lists are difficult to compute. More complicated games such as chess have more possible strategies that there are molecules in the universe. A normal form game already has a complete list of all possible combinations of strategies and payoffs, thus removing the element of player choices. In short, in a normal form game, the best move is always known.

1. Dauben, Joseph W "Game Theory." Microsoft Encarta. Microsoft Corp, 1999
2. McCain, Roger A. "Game Theory: An Introductory Sketch." Hypertext. 1999 (August 1999)