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If a strictly dominant strategy exists for one player in a game, that player will play that strategy in each of the game's Nash equilibria.If both players have a strictly dominant strategy, the game has only one unique Nash equilibrium, referred to as a "dominant strategy equilibrium".
This technique can identify dominant strategies where a player can identify an action that they can take no matter what the competitor does to try to maximize the payoff. A strategy profile (sometimes called a strategy combination) is a set of strategies for all players which fully specifies all actions in a game. A strategy profile must ...
If both A and B have strictly dominant strategies, there exists a unique Nash equilibrium in which each plays their strictly dominant strategy. In games with mixed-strategy Nash equilibria, the probability of a player choosing any particular (so pure) strategy can be computed by assigning a variable to each strategy that represents a fixed ...
A payoff function for a player is a mapping from the cross-product of players' strategy spaces to that player's set of payoffs (normally the set of real numbers, where the number represents a cardinal or ordinal utility—often cardinal in the normal-form representation) of a player, i.e. the payoff function of a player takes as its input a ...
The problem of finding an optimal strategy in a differential game is closely related to the optimal control theory. In particular, there are two types of strategies: the open-loop strategies are found using the Pontryagin maximum principle while the closed-loop strategies are found using Bellman's Dynamic Programming method.
For player two, they will choose their moves based on the two row strategies. Assuming both players do not know the opponents strategies. [10] It is a dominant strategy for the first player to choose a payoff of 5 rather than a payoff of 3 because strategy D is a better response than strategy C.
A dominant strategy provides a player with the highest possible payoff for any strategy of the other players. In simultaneous games, the best move a player can make is to follow their dominant strategy, if one exists. [11] When analyzing a simultaneous game: Firstly, identify any dominant strategies for all players.
A dominant strategy is a strategy that is always the most likely to lead to success, making it objectively the best strategy. This therefore renders all related decisions meaningless. Even if a strategy does not always win, but clearly is the best, it can be called (almost) dominant.