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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".
While Nash proved that every finite game has a Nash equilibrium, not all have pure strategy Nash equilibria. For an example of a game that does not have a Nash equilibrium in pure strategies, see Matching pennies. However, many games do have pure strategy Nash equilibria (e.g. the Coordination game, the Prisoner's dilemma, the Stag hunt ...
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 ...
The standard representations of chicken, the prisoner's dilemma, and the stag hunt are all symmetric games. The most commonly studied asymmetric games are games where there are not identical strategy sets for both players. For instance, the ultimatum game and similarly the dictator game have different strategies for each player. It is possible ...
Some games have multiple weak dictators (in rock-paper-scissors both players are weak dictators but none is a strong dictator). Also see Effectiveness. Antonym: dummy. Dominated outcome Given a preference ν on the outcome space, we say that an outcome a is dominated by outcome b (hence, b is the dominant strategy) if
Games can have several features, a few of the most common are listed here. Number of players: Each person who makes a choice in a game or who receives a payoff from the outcome of those choices is a player. Strategies per player: In a game each player chooses from a set of possible actions, known as pure strategies. If the number is the same ...
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 Nash equilibrium is a strategy profile (a strategy profile specifies a strategy for every player, e.g. in the above prisoners' dilemma game (cooperate, defect) specifies that prisoner 1 plays cooperate and prisoner 2 plays defect) in which every strategy played by every agent (agent i) is a best response to every other strategy played by all the other opponents (agents j for every j≠i) .