A pure strategy is a term used to refer to strategies in Game theory. Each player is given a set of strategies, if a player chooses to take one action with probability 1 then that player is playing a pure strategy. This is in contrast to a mixed strategy where individual players choose a probability distribution over several actions. Game theory is a branch of applied mathematics that uses models to study interactions with formalised incentive structures (games). It has applications in a variety of fields, including economics, international relations, evolutionary biology, political science, and military strategy. ... A mixed strategy is used in game theory economics to describe a strategy compromising of possible moves and a probability distribution which corresponds to how frequently each move is chosen. ...

Illustration

Suppose the following payoff matrix (known as a Coordination game): A payoff matrix or payoff function is a concept in game theory which shows what payoff each player will receive at the outcome of the game. ... In game theory, the Nash equilibrium (named after John Nash) is a kind of optimal strategy for games involving two or more players, whereby the players reach an outcome to mutual advantage. ...

Here one player chooses the row and the other chooses a column. The row player receives the first payoff, the column the second. If row opts to play A with probability 1 (i.e. play 1 for sure), then he is said to be playing a pure strategy. If column opts to flip a coin and play A if the coin lands heads and B if the coin lands tails, then she is said to be playing a mixed strategy not a pure strategy.

Significance

In his famous paper John Forbes Nash proved that there is a Nash equilibrium (not his term) for every finite game. One can divide Nash equilbria into two types. Pure strategy Nash equilibria are Nash equilibria where all players are playing pure strategies. Mixed strategy Nash equilibria are equilibria where at least one player is playing a mixed strategy. While Nash proved that every finite game has a Nash equilibria, not all have pure strategy Nash equilibria. For an example of a game that does not have a Nash equilibrium in pure strategies see Rock paper scissors. However, many games do have pure strategy Nash equilibria (e.g. the Coordination game, the Prisoner's dilemma, the Stag hunt, etc.). John Forbes Nash John Forbes Nash Jr. ... In game theory, the Nash equilibrium (named after John Nash) is a kind of optimal strategy for games involving two or more players, where no player has anything to gain by changing only his own strategy. ... Rock, Paper, Scissors chart Rock, Paper, Scissors (sometimes with the elements in its name permuted and/or Rock replaced with Stone and/or Paper with Cloth, but also known as Roshambo, Rochambeau, Ick-Ack-Ock, Janken, Mora, Morra Cinese, Gawi-Bawi-Bo, JanKenPon or Farkle) is a popular hand game... In game theory, the Nash equilibrium (named after John Nash) is a kind of optimal strategy for games involving two or more players, whereby the players reach an outcome to mutual advantage. ... Will the two prisoners cooperate to minimise total loss of liberty or will one of them, trusting the other to cooperate, betray him so as to go free? The prisoners dilemma is a type of non-zero-sum game (game in the sense of Game Theory). ... In game theory, the Stag Hunt is a game first discussed by Jean-Jacques Rousseau. ...