Pure strategy

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A pure strategy is a term used to refer to strategies in Game theory. Each player is given a set of strategies, if a player chooses to take one action with probability 1 then that player is playing a pure strategy. This is in contrast to a mixed strategy where individual players choose a probability distribution over several actions.

[edit] Illustration

Pure coordination game

	A	B
A	1, 1	0, 0
B	0, 0	1, 1

Suppose the payoff matrix pictured to the right (known as a coordination game). Here one player chooses the row and the other chooses a column. The row player receives the first payoff, the column the second. If row opts to play A with probability 1 (i.e. play A for sure), then he is said to be playing a pure strategy. If column opts to flip a coin and play A if the coin lands heads and B if the coin lands tails, then she is said to be playing a mixed strategy not a pure strategy.

[edit] Significance

In his famous paper John Forbes Nash proved that there is a Nash equilibrium (not his term) for every finite game. One can divide Nash equilibria into two types. Pure strategy Nash equilibria are Nash equilibria where all players are playing pure strategies. Mixed strategy Nash equilibria are equilibria where at least one player is playing a mixed strategy. While Nash proved that every finite game has a Nash equilibrium, not all have pure strategy Nash equilibria. For an example of a game that does not have a Nash equilibrium in pure strategies see Rock paper scissors. However, many games do have pure strategy Nash equilibria (e.g. the Coordination game, the Prisoner's dilemma, the Stag hunt). Further, games can have both pure strategy and mixed strategy equilibria.

v·d·e Topics in game theory
Definitions	Normal-form game · Extensive-form game · Cooperative game · Information set · Preference
Equilibrium concepts	Nash equilibrium · Subgame perfection · Bayesian-Nash · Perfect Bayesian · Trembling hand · Proper equilibrium · Epsilon-equilibrium · Correlated equilibrium · Sequential equilibrium · Quasi-perfect equilibrium · Evolutionarily stable strategy · Risk dominance · Pareto efficiency
Strategies	Dominant strategies · Pure strategy · Mixed strategy · Tit for tat · Grim trigger · Collusion · Backward induction
Classes of games	Symmetric game · Perfect information · Dynamic game · Sequential game · Repeated game · Signaling game · Cheap talk · Zero-sum game · Mechanism design · Bargaining problem · Stochastic game · Nontransitive game · Global games
Games	Prisoner's dilemma · Traveler's dilemma · Coordination game · Chicken · Volunteer's dilemma · Dollar auction · Battle of the sexes · Stag hunt · Matching pennies · Ultimatum game · Minority game · Rock-paper-scissors · Pirate game · Dictator game · Public goods game · Blotto games  ·War of attrition  ·El Farol Bar problem  ·Cake cutting  ·Cournot game  ·Deadlock  ·Diner's dilemma  ·Guess 2/3 of the average  ·Kuhn poker  ·Nash bargaining game  ·Screening game  ·Signaling game  ·Trust game  ·Princess and monster game
Theorems	Minimax theorem · Purification theorem · Folk theorem · Revelation principle · Arrow's impossibility theorem

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This page uses content from the English-language version of Wikipedia. The original article was at Pure strategy. The list of authors can be seen in the page history. As with Psychology Wiki, the text of Wikipedia is available under the GNU Free Documentation License.