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Algorithmic game theory (AGT) is an area in the intersection of game theory and computer science, with the objective of understanding and design of algorithms in strategic environments. Typically, in Algorithmic Game Theory problems, the input to a given algorithm is distributed among many players who have a personal interest in the output.
A solved game is a game whose outcome (win, lose or draw) can be correctly predicted from any position, assuming that both players play perfectly.This concept is usually applied to abstract strategy games, and especially to games with full information and no element of chance; solving such a game may use combinatorial game theory or computer assistance.
An animated pedagogical example showing the plain negamax algorithm (that is, without alpha–beta pruning). The person performing the game tree search is considered to be the one that has to move first from the current state of the game (player in this case) NegaMax operates on the same game trees as those used with the minimax search ...
General game playing (GGP) is the design of artificial intelligence programs to be able to play more than one game successfully. [1] [2] [3] For many games like chess, computers are programmed to play these games using a specially designed algorithm, which cannot be transferred to another context.
An impartial game is one in which at any given point in the game, each player is allowed exactly the same set of moves. Normal-play nim is an example of an impartial game. In nim, there are one or more heaps of objects, and two players (we'll call them Alice and Bob), take turns choosing a heap and removing 1 or more objects from it.
The introductory text Winning Ways introduced a large number of games, but the following were used as motivating examples for the introductory theory: . Blue–Red Hackenbush - At the finite level, this partisan combinatorial game allows constructions of games whose values are dyadic rational numbers.
Bruce Ballard was the first to develop a technique, called *-minimax, that enables alpha-beta pruning in expectiminimax trees. [3] [4] The problem with integrating alpha-beta pruning into the expectiminimax algorithm is that the scores of a chance node's children may exceed the alpha or beta bound of its parent, even if the weighted value of each child does not.
In game theory, Zermelo's theorem is a theorem about finite two-person games of perfect information in which the players move alternately and in which chance does not affect the decision making process. It says that if the game cannot end in a draw, then one of the two players must have a winning strategy (i.e. can force a win).