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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.
Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets , which became a standard method in game theory and mathematical economics .
Constant sum: A game is a constant sum game if the sum of the payoffs to every player are the same for every single set of strategies. In these games, one player gains if and only if another player loses. A constant sum game can be converted into a zero sum game by subtracting a fixed value from all payoffs, leaving their relative order unchanged.
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 game theory, the Nash equilibrium is the most commonly-used solution concept for non-cooperative games.A Nash equilibrium is a situation where no player could gain by changing their own strategy (holding all other players' strategies fixed). [1]
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 ...
A strategy game is a game that relies primarily on strategy, and when it comes to defining what strategy is, two factors need to be taken into account: its complexity and game-scale actions, such as each placement in the Total War video game series. The definition of a strategy game in its cultural context should be any game that belongs to a ...
The normal-form representation of a game includes all perceptible and conceivable strategies, and their corresponding payoffs, for each player. In static games of complete, perfect information, a normal-form representation of a game is a specification of players' strategy spaces and payoff functions. A strategy space for a player is the set of ...