The Game Theory

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Game Theory is a branch of applied mathematics. Game theory concepts are applied whenever the actions of individuals, groups, firms or any combination of these are interdependent. It is a formal study of decision making where players must make choices that potentially affects interests of other players.


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. ...
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