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, mixed and/or strategies:
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Bright jewels of the mine?
The wealthy of seas, the spoils of war?—
They sought a faith’s pure shrine!
Ay, call it holy ground,
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They have left unstained what there they found,—
Freedom to worship God.”
—Felicia Dorothea Hemans (1783–1835)
“When truth is nothing but the truth, it’s unnatural, it’s an abstraction that resembles nothing in the real world. In nature there are always so many other irrelevant things mixed up with the essential truth. That’s why art moves you—precisely because it’s unadulterated with all the irrelevancies of real life.”
—Aldous Huxley (1894–1963)
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—Frances Fitzgerald (b. 1940)