The Game Theory - Essay Example

The games are well defined mathematical objects where it consists of a set of players, a set of strategies (moves) available to players and specification of payoffs for combination of strategies. A player is said to be rational if he play in a manner which maximizes his own payoff. It is often assumed that rationality of all players is common knowledge. A strategy dominates another strategy of a player if it gives a better payoff to that player, irrespective of what the other players are doing.

For example, if a player have two strategies A and B the outcome resulting from A is better than that of B, then strategy A is said to dominate strategy B. A rational player will never choose to play a dominated strategy. In an extensive game, a strategy is a complete plan of choices, one for each decision point of the player. A mixed strategy is an active randomization, with given probabilities, that determine the players decision. The games are splitted as cooperative and noncooperative games.

In a noncooperative game the participants cannot make commitments to coordinate their strategies, and hence the solution is a noncoopoerative solution. In a noncooperative game with finite players Nash equilibrium is a set of mixed strategies between two or more players where no player can improve his payoff by changing his strategy. Noncooperative games are defined by extensive and normal forms whereas cooperative games are presented in characteristic function form. In extensive form, games are often represented as trees and each node (vertex) represent a point of choice for a player.

Each player is represented by a vertex. The lines out of vertex denote possible action for that player and the payoffs are specified at the bottom of the tree. In the normal form (or strategic form) game is represented by a matrix which tells strategies, players and payoffs. In general it is represented by any function that associates a payoff for each player with every possible combination of actions. In the normal form it is assumed that each player acts simultaneously without knowing the action of other.

In cooperative games the individual payoffs of player are not known but the characteristic function gives the payoff of each coalition. For empty coalition the payoff is considered to be 0. In partition function form the payoffs not only depend on its members but also on the rest of players who were partitioned. In cooperative game participants can make commitments to coordinate their strategy which is a converse to noncooperative games. Cooperative games are particularly used in economics.

In cooperative games if side payments (incentives) are allowed then the corresponding solution concept is known as transferable utility cooperative value otherwise it is known as nontransferable utility cooperative value. In game theory we have zero sum and non zero sum games. In zero sum games, the players gain or loss is balanced by other players losses or gains so that the total gains obtained when subtracted with total losses of the players gives a zero sum. In nonzero sum games we have sum less than or more than zero.

A game is said to be sequential if one player performs his action after another or else it is a simultaneous move game. An example for a zero sum game is Matching pennies. In this game we have two players having a penny. On tossing the