Concepts inThe complexity of computing a Nash equilibrium
PPAD (complexity)
PPAD ("Polynomial Parity Arguments on Directed graphs") is a complexity class introduced by Christos Papadimitriou in 1994. PPAD is a subclass of TFNP based on functions that can be shown to be total by a parity argument. The class attracted significant attention in the field of algorithmic game theory because it contains the problem of computing a Nash equilibrium, and this problem was shown by Chen and Deng in 2005 to be complete for the class.
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Nash equilibrium
In game theory, Nash equilibrium (named after John Forbes Nash, who proposed it) is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally.
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Normal-form game
In game theory, normal form is a description of a game. Unlike extensive form, normal-form representations are not graphical per se, but rather represent the game by way of a matrix. While this approach can be of greater use in identifying strictly dominated strategies and Nash equilibria, some information is lost as compared to extensive-form representations.
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Complexity class
In computational complexity theory, a complexity class is a set of problems of related resource-based complexity. A typical complexity class has a definition of the form: the set of problems that can be solved by an abstract machine M using O(f) of resource R, where n is the size of the input.
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Game theory
Game theory is the study of strategic decision making. More formally, it is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers. " An alternative term suggested "as a more descriptive name for the discipline" is interactive decision theory. Game theory is mainly used in economics, political science, and psychology, as well as logic and biology.
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In computational complexity theory, a computational problem is complete for a complexity class if it is, in a technical sense, among the "hardest" (or "most expressive") problems in the complexity class. More formally, a problem p is called hard for a complexity class C under a given type of reduction, if there exists a reduction (of the given type) from any problem in C to p.
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Time complexity
In computer science, the time complexity of an algorithm quantifies the amount of time taken by an algorithm to run as a function of the size of the input to the problem. The time complexity of an algorithm is commonly expressed using big O notation, which suppresses multiplicative constants and lower order terms. When expressed this way, the time complexity is said to be described asymptotically, i.e. , as the input size goes to infinity.
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