2. John Forbes Nash John Forbes Nash, Jr. (born June 13, 1928) is an American mathematician whose works in game theory, differential geometry, and partial differential equations have provided insight into the factors that govern chance and events inside complex systems in daily life. His theories are used in market economics, computing, evolutionary biology, artificial intelligence, accounting, politics and military theory.

4. Nash is the subject of the 2001 Hollywood movie A Beautiful Mind. The film, loosely based on the biography of the same name, focuses on Nash's mathematical genius and also his schizophrenia. Nash earned a doctorate in 1950 with a 28- page dissertation on non-cooperative games. The thesis, which was written under the supervision of doctoral advisor Albert W. Tucker, contained the definition and properties of what would later be called the "Nash equilibrium". It is a crucial concept in non-cooperative games, and it won Nash the Nobel prize in economics in 1994.

5.  If a decision, if the best land what do you do if the other players called the dominant strategy of game theory language.. Each solution is a dominant strategy Nash solution, but the converse is not true.. Theory can be summed up in a simple way: if all players are directed to the same destination, which will reduce the probability of obtaining these players; The orientation will increase to different destinations.

6. That is a theoretical analysis can be applied in two specific cases: A player gains derived by the other (or others) in absolute contradiction created by the loss of status. Mixed case of cooperation with the contradictions that follows, in which case players can login to cooperate in order to increase their joint profits, but is still a contradiction in the earnings distribution.

8.  Game theory is a study of strategic decision making. Specifically, it is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers" Game theory is mainly used in economics, political science, and psychology, as well as logic, computer science, and biology.  The subject first addressed zero-sum games, such that one person's gains exactly equal net losses of the other participant or participants. Modern game theory began with the idea regarding the existence of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann.

9. Zero-sum model (John von Neumann); one of the parties in this model means that the direct loss of income to another. During the cold war there is such a relationship in terms of the great powers. If you try to find the most rational strategy even in such a case, one party's own terms "the best" by selecting able to capture a balance point. Non-zero-sum model (John F. Nash); This model, although still mainly rival parties to each other, it may also be profitable for both sides to the question of balance

10. Representation of games The games studied in game theory are well- defined mathematical objects. To be fully defined, a game must specify the following elements: the players of the game, the information and actions available to each player at each decision point, and the payoffs for each outcome. (Rasmusen refers to these four "essential elements" by the acronym "PAPI". A game theorist typically uses these elements, along with a solution concept of their choosing, to deduce a set of equilibrium strategies for each player such that, when these strategies are employed, no player can profit by unilaterally deviating from their strategy

11. These equilibrium strategies determine an equilibrium to the game a stable state in which either one outcome occurs or a set of outcomes occur with known probability. Most cooperative games are presented in the characteristic function form, while the extensive and the normal forms are used to define noncooperative games.

12. Extensive form  The extensive form can be used to formalize games with a time sequencing of moves. Games here are played on trees.Here each vertex (or node) represents a point of choice for a player. The player is specified by a number listed by the vertex. The lines out of the vertex represent a possible action for that player. The payoffs are specified at the bottom of the tree. The extensive form can be viewed as a multi-player generalization of a decision tree.

13.  In the game pictured to the left, there are two players. Player 1 moves first and chooses either F or U. Player 2 sees Player 1's move and then chooses A or R. Suppose that Player 1 chooses U and then Player 2 chooses A, then Player 1 gets 8 and Player 2 gets 2. The extensive form can also capture simultaneous-move games and games with imperfect information. To represent it, either a dotted line connects different vertices to represent them as being part of the same information set or a closed line is drawn around them.

14. Normal form game The normal (or strategic form) game is usually represented by a matrix which shows the players, strategies, and payoffs (see the example to the right). More generally it can be represented by any function that associates a payoff for each player with every possible combination of actions. In the accompanying example there are two players; one chooses the row and the other chooses the column. Each player has two strategies, which are specified by the number of rows and the number of columns.

15.  The payoffs are provided in the interior. The first number is the payoff received by the row player (Player 1 in our example); the second is the payoff for the column player (Player 2 in our example). Suppose that Player 1 plays Up and that Player 2 plays Left. Then Player 1 gets a payoff of 4, and Player 2 gets 3.

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