Pure strategy

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In game theory, pure strategy is a strategy in which the player has clearly determined his strategy.

classification

The pure strategy is often seen as the counterpart to the mixed strategy , although this is only a special case of the mixed strategy in the game. The player decides on a strategy and applies it repeatedly. Mixed strategies arise from the combination ( randomization ) of pure strategies and their random, unspecified application.

example

Coin game ("heads" or "tails") Player 1 and player 2 each place a coin. Player 1 wins if the coins placed show both “heads” or both “tails”. Player 2 wins if the coin sides are different.

For a player who z. For example, if you pursue a pure strategy (e.g. commit yourself to “heads”) and exclude all others (“tails”), you choose the probability of 1 for this strategy and the probability of zero for the other. If, on the other hand, a player perceives both strategies and randomly decides between the pure strategies (ie “heads” or “tails”), his strategy is described as (0.5; 0.5). The player follows a mixed strategy.

In the course of the game, this has the following consequences: In simple games without repetition, it is easy to pursue a pure strategy. Player 1 wins if player 2 also lays "heads" or loses if player 2 lays "tails". If the games are repeated, however, following a pure strategy turns out to be disadvantageous for player 1, since the opposing player will adapt to the strategy of player 1 in order to be successful (player 2 would therefore always place “tails”). Pursuing one of the two pure strategies “heads” or “tails” would not make sense.

A mix of pure strategies is therefore appropriate. The combination of the pure strategies by player 1 forces player 2 to adapt. A balance of the strategies is inevitably established when "heads" and "tails" are placed randomly and the sides of the coin are applied equally, which is described in the Min-Max theorem .

application

Pure strategies have little success in games of chance (heads or tails, rock-paper-scissors ). These are easy to see through and the opposing player can adapt accordingly if the game continues, i.e. is repeated. It is more successful to use mixed strategies by making a random choice . Pure strategies are therefore more likely to be used in business, for example when deciding whether a product should be manufactured or not, or whether the advertising budget should be increased or decreased.

literature

supporting documents

  1. ↑ 1.Manfred J. Holler Gerhard Illing: Introduction to Game Theory, p 11, Springer Verlag, Heidelberg, 2006, ISBN 3-540-27880-X .
  2. ↑ 1.Manfred J. Holler Gerhard Illing: Introduction to Game Theory, p 34, Springer Verlag, Heidelberg, 2006, ISBN 3-540-27880-X .
  3. ↑ 1.Manfred J. Holler Gerhard Illing: Introduction to Game Theory, p 35, Springer Verlag, Heidelberg, 2006, ISBN 3-540-27880-X .
  4. ↑ Robert S. Pindyck / Daniel L. Rubinfeld: Microeconomics , p 662, Pearson Education, Munich, 2003, ISBN 3-8273-7025-6 .