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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).
Parrondo's paradox, a paradox in game theory, has been described as: A combination of losing strategies becomes a winning strategy. [1] It is named after its creator, Juan Parrondo, who discovered the paradox in 1996.
The work of John von Neumann established game theory as its own independent field in the early-to-mid 20th century, with von Neumann publishing his paper On the Theory of Games of Strategy in 1928. [ 10 ] [ 11 ] Von Neumann's original proof used Brouwer's fixed-point theorem on continuous mappings into compact convex sets , which became a ...
This game is a common demonstration in game theory classes. It reveals the significant heterogeneity of behaviour. [11] It is unlikely that many people will play rationally according to the Nash equilibrium. This is because the game has no strictly dominant strategy, so it requires players to consider what others will do.
The first book in the series was published in 2010, with the two sequels, The Fractal Prince and The Causal Angel, published in 2012 and 2014, respectively. A game modeled after the iterated prisoner's dilemma is a central focus of the 2012 video game Zero Escape: Virtue's Last Reward and a minor part in its 2016 sequel Zero Escape: Zero Time ...
In applied game theory, the definition of the strategy sets is an important part of the art of making a game simultaneously solvable and meaningful. The game theorist can use knowledge of the overall problem, that is the friction between two or more players, to limit the strategy spaces, and ease the solution.
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.
In descriptive set theory, the Borel determinacy theorem states that any Gale–Stewart game whose payoff set is a Borel set is determined, meaning that one of the two players will have a winning strategy for the game. A Gale–Stewart game is a possibly infinite two-player game, where both players have perfect information and no randomness is ...