Strategy (game theory)#Pure and mixed strategies

The pure strategy in game theory, a strategy in which the player has clearly determined its strategy.

Classification

The pure strategy is often seen as a counterpart to the mixed strategy, although this represents only a special case of the mixed strategy in the game. The player doing commits itself to a strategy and applies them repeatedly. Mixed strategies are created by combining ( randomization) of pure strategies and their random non- specified application.

Example

Slots game ( "head" or " number" ) Player 1 and Player 2 each define a coin. Player 1 wins if the set coins show both "head" or both " number". Player 2 wins if the Münzseiten are different.

For example, a player of the a pure strategy pursued ( eg, lies down on "head" fixed) and the exclusion of others ( " number" ), selected for this strategy, the probability of 1 and for the other, the probability of zero. Other hand, a player takes both strategies and true (ie "head" or " number" ) chooses randomly between the pure strategies, then describes his strategy with (0.5, 0.5 ). The player is pursuing a mixed strategy.

During the game has the following consequences: For simple games without repeating the pursuit of a pure strategy is easily feasible. Player 1 wins if player 2 also "head" sets or loses when player places 2 " number". Are the games but repeatedly, the pursuit of a pure strategy proves to be disadvantageous for the player 1, since the opposing player will adapt to the strategy of player 1 in order to succeed (player 2 would therefore always " number" set ). The pursuit of one of the two pure strategies "head" or " number" would not make sense.

A mix of pure strategies is therefore appropriate. The combination of pure strategies by Player 1 Player 2 is forced to adapt. A balance of strategies inevitably raises at a random place of "head" and " number" under an equal application of the frequent Münzseiten a what is described in the min-max theorem.

Application

Pure strategies have in games ( heads or tails, rock -paper-scissors ) with little success. These are easy to see through and the opposing player is able to adapt accordingly if the game continued to play, ie is repeated. Successful is the use of mixed strategies by a random choice is made. Application therefore find pure strategies rather in the economy, for example, in the decision whether or not a product is to be produced, or if the advertising budget is to be increased or decreased.