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Game theory is the study of mathematical models of strategic interactions. [1] It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. [2] Initially, game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly balanced by ...
Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Study has been largely confined to two-player games that have a position that the players take turns changing in defined ways or moves to achieve a defined winning condition.
Proposed by. John Forbes Nash Jr. Used for. All non-cooperative games. In game theory, the Nash equilibrium is the most commonly-used solution concept for non-cooperative games. A Nash equilibrium is a situation where no player could gain by changing their own strategy (holding all other players' strategies fixed). [1]
Mathematics. Pure mathematics studies the properties and structure of abstract objects, [1] such as the E8 group, in group theory. This may be done without focusing on concrete applications of the concepts in the physical world. Pure mathematics is the study of mathematical concepts independently of any application outside mathematics.
The game of Go is one of the most popular games in the world. As a result of its elegant and simple rules, the game has long been an inspiration for mathematical research. Shen Kuo, an 11th century Chinese scholar, estimated in his Dream Pool Essays that the number of possible board positions is around 10 172.
In game theory, folk theorems are a class of theorems describing an abundance of Nash equilibrium payoff profiles in repeated games ( Friedman 1971 ). [1] The original Folk Theorem concerned the payoffs of all the Nash equilibria of an infinitely repeated game. This result was called the Folk Theorem because it was widely known among game ...
In mathematics, class field theory ( CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global fields using objects associated to the ground field. [1] Hilbert is credited as one of pioneers of the notion of a class field. However, this notion was already familiar ...
Sequential game: A game is sequential if one player performs their actions after another player; otherwise, the game is a simultaneous move game. Perfect information: A game has perfect information if it is a sequential game and every player knows the strategies chosen by the players who preceded them. Constant sum: A game is a constant sum ...