An Introduction to Game Theory

An Introduction to Game Theory comprises information on the concept of Game Theory, its application and the various forms of games that the theory propounds. It is basically a theory of strategies where the agents indulge themselves in choosing the right combination of action to maximize the profit at the end of the game. These agents interact among themselves in the given situation. The situation normally is a conflicting one.

An Introduction to Game Theory comprises information on the concept of Game Theory, its application and the various forms of games that the theory propounds. It is basically a theory of strategies where the agents indulge themselves in choosing the right combination of action to maximize the profit at the end of the game. These agents interact among themselves in the given situation. The situation normally is a conflicting one.

Playing the Game

The games propounded by the theory are properly defined mathematical objects. It comprises of a set of players, a set of strategies and payoffs for the strategies.

The Extensive form of the game is employed to formalize games with significant order. Tree is the symbolic representation of the game where each vertex stands for a point of selection for a player; a specific number is allotted to the player. The lines stemming out of the vertex symbolizes a set of action for the player and the payoffs are given at the bottom of the tree. There could be more than two agents in the game. At last a dotted line joins the vertices as part of the set of information.

A matrix where the players, strategies and payoffs are all laid within it defines the Normal form of Game. It is a two-agent game where players are allotted two strategies and these are represented by the rows and columns each player select. Unlike the previous game here the payoff is specified in the interior. None of the players are aware of the opponent’s strategies in the normal form of game. The Function form of Game is a part of the cooperative form of game. There are no individual payoffs in this game as one player is able to transfer its utility to the other player. The payoffs are in coalition. The empty coalition is assumed to obtain zero payoff. The seminal book of Von Neumann and Morgenstern talks about this model of game. It assumes that a coalition represented as C plays against a complimentary coalition represented as (N/C), the characteristic is the equilibrium payoff of C. the Function Game is formally referred to as the TU (Total Utility) Game and is represented as a pair (N,v) where N stands for a set of players and v : 2n = R is a characteristic function. Lastly, the Partition Function form takes into account the way in which the rest of the players are partitioned besides its members while deciding on the coalition payoff.

Types of Games

There are various types of Games. They are:

• Cooperative Games where the players from bonds
• Symmetric and Asymmetric Game where the payoff one strategy determines payoff of another strategy and not on the players
• Zero Sum and Non-Zero Sum where the selection of players do not affect the resources
• Simultaneous and Sequential games are game forms where the players move simultaneously
• Perfect Information and Imperfect Information where the players either know or do not know the combinations
• Infinitely Long Games where the moves are not complete

  Economists have successfully applied the Game Theory in analyzing economic phenomenon like bargaining, voting systems, duopolies, fair division, social network, auctions. They follow two methods of application. They are the Descriptive Method and the Prescriptive or Normative method.