Pure and Mixed Strategies
A pure strategy provides a complete definition of how a player will play a game. In particular, it determines the move a player will make for any situation he or she could face. A player's strategy set is the set of pure strategies available to that player.
A mixed strategy is an assignment of a probability to each pure strategy. This allows for a player to randomly select a pure strategy. Since probabilities are continuous, there are infinitely many mixed strategies available to a player, even if their strategy set is finite.
Of course, one can regard a pure strategy as a degenerate case of a mixed strategy, in which that particular pure strategy is selected with probability 1 and every other strategy with probability 0.
A totally mixed strategy is a mixed strategy in which the player assigns a strictly positive probability to every pure strategy. (Totally mixed strategies are important for equilibrium refinement such as trembling hand perfect equilibrium.)
Read more about this topic: Strategy (game Theory)
Famous quotes containing the words pure and, pure, mixed and/or strategies:
“No advantages in this world are pure and unmixed.”
—David Hume (1711–1776)
“Examinations, sir, are pure humbug from beginning to end. If a man is a gentleman, he knows quite enough, and if he is not a gentleman, whatever he knows is bad for him.”
—Oscar Wilde (1854–1900)
“Mrs. Finney: Can’t we have some peace in this house, even on New Year’s Eve?
Sadie: You got it mixed up with Christmas. New Year’s Eve is when people go back to killing each other.”
—Joseph L. Mankiewicz (1909–1993)
“By intervening in the Vietnamese struggle the United States was attempting to fit its global strategies into a world of hillocks and hamlets, to reduce its majestic concerns for the containment of communism and the security of the Free World to a dimension where governments rose and fell as a result of arguments between two colonels’ wives.”
—Frances Fitzgerald (b. 1940)