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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).
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.
The multiplicative weights update method is an algorithmic technique most commonly used for decision making and prediction, and also widely deployed in game theory and algorithm design. The simplest use case is the problem of prediction from expert advice, in which a decision maker needs to iteratively decide on an expert whose advice to follow.
MuZero (MZ) is a combination of the high-performance planning of the AlphaZero (AZ) algorithm with approaches to model-free reinforcement learning. The combination allows for more efficient training in classical planning regimes, such as Go, while also handling domains with much more complex inputs at each stage, such as visual video games.
After four hours of training, DeepMind estimated AlphaZero was playing chess at a higher Elo rating than Stockfish 8; after nine hours of training, the algorithm defeated Stockfish 8 in a time-controlled 100-game tournament (28 wins, 0 losses, and 72 draws). [2] [3] [4] The trained algorithm played on a single machine with four TPUs.
Two-person games can also be represented as and-or trees. For the first player to win a game, there must exist a winning move for all moves of the second player. This is represented in the and-or tree by using disjunction to represent the first player's alternative moves and using conjunction to represent all of the second player's moves.
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 algorithm. Each node and root node in the tree are game states (such as game board configuration) of a two player game.
The algorithm can be implemented to run in time quadratic in the number of participants, and linear in the size of the input to the algorithm. The stable matching problem, and the Gale–Shapley algorithm solving it, have widespread real-world applications, including matching American medical students to residencies and French university ...