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A subfield of set theory that examines the conditions under which one or the other player of a game has a winning strategy, and the consequences of the existence of such strategies. Games studied in set theory are Gale–Stewart games – two-player games of perfect information in which the players make an infinite sequence of moves and there ...
Selected equilibrium refinements in game theory. Arrows point from a refinement to the more general concept (i.e., ESS Proper). In game theory, a solution concept is a formal rule for predicting how a game will be played. These predictions are called "solutions", and describe which strategies will be adopted by players and, therefore, the ...
Separately, game theory has played a role in online algorithms; in particular, the k-server problem, which has in the past been referred to as games with moving costs and request-answer games. [125] Yao's principle is a game-theoretic technique for proving lower bounds on the computational complexity of randomized algorithms , especially online ...
In game theory, a strictly determined game is a two-player zero-sum game that has at least one Nash equilibrium with both players using pure strategies.The value of a strictly determined game is equal to the value of the equilibrium outcome.
A classic example of a dynamic game with types is a war game where the player is unsure whether their opponent is a risk-taking "hawk" type or a pacifistic "dove" type. Perfect Bayesian Equilibria are a refinement of Bayesian Nash equilibrium (BNE), which is a solution concept with Bayesian probability for non-turn-based games.
A key property of a strategy-stealing argument is that it proves that the first player can win (or possibly draw) the game without actually constructing such a strategy. So, although it might prove the existence of a winning strategy, the proof gives no information about what that strategy is.
In game theory, a repeated game (or iterated game) is an extensive form game that consists of a number of repetitions of some base game (called a stage game). The stage game is usually one of the well-studied 2-person games. Repeated games capture the idea that a player will have to take into account the impact of their current action on the ...
In game theory, a Bayesian game is a strategic decision-making model which assumes players have incomplete information. Players may hold private information relevant to the game, meaning that the payoffs are not common knowledge. [1] Bayesian games model the outcome of player interactions using aspects of Bayesian probability.