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:
“Who knows whither the clouds have fled?
In the unscarred heaven they leave no wake,
And the eyes forget the tears they have shed,
The heart forgets its sorrow and ache;
The soul partakes the season’s youth,
And the sulphurous rifts of passion and woe
Lie deep ‘neath a silence pure and smooth,
Like burnt-out craters healed with snow.”
—James Russell Lowell (1819–1891)
“But I hate things all fiction ... there should always be some foundation of fact for the most airy fabric—and pure invention is but the talent of a liar.”
—GGeorge Gordon Noel Byron (1788–1824)
“Memory is a wonderfully useful tool, and without it judgement does its work with difficulty; it is entirely lacking in me.... Now, the more I distrust my memory, the more confused it becomes. It serves me better by chance encounter; I have to solicit it nonchalantly. For if I press it, it is stunned; and once it has begun to totter, the more I probe it, the more it gets mixed up and embarrassed. It serves me at its own time, not at mine.”
—Michel de Montaigne (1533–1592)
“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)