strategy
A pure strategy provides a definition for a way a player can play a game. In particular, it defines, for every possible choice a player might have to make, which option the player picks. A player’s strategy space is the set of pure strategies available to that player.
A mixed strategy is an assignment of a probability to each pure strategy. It defines a probability over the strategies, and reflect that, rather than choosing a particular pure strategy, the player will randomly select a pure strategy based on the distribution^{} given by their mixed strategy. Of course, every pure strategy is a mixed strategy (the function which takes that strategy to $1$ and every other one to $0$).
The following notation is often used:

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${S}_{i}$ for the strategy space of the $i$th player

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${s}_{i}$ for a particular element of ${S}_{i}$; that is, a particular pure strategy

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${\sigma}_{i}$ for a mixed strategy. Note that ${\sigma}_{i}\in {S}_{i}\to [0,1]$ and ${\sum}_{{s}_{i}\in {S}_{i}}{\sigma}_{i}({s}_{i})=1$.

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${\mathrm{\Sigma}}_{i}$ for the set of all possible mixed strategies for the $i$th player

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$S$ for ${\prod}_{i}{S}_{i}$, the set of all possible of pure strategies (essentially the possible outcomes of the game)

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$\mathrm{\Sigma}$ for ${\prod}_{i}{\mathrm{\Sigma}}_{i}$

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$\sigma $ for a strategy profile, a single element of $\mathrm{\Sigma}$

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${S}_{i}$ for ${\prod}_{j\ne i}{S}_{j}$ and ${\mathrm{\Sigma}}_{i}$ for ${\prod}_{j\ne i}{\mathrm{\Sigma}}_{j}$, the sets of possible pure and mixed strategies for all players other than $i$.

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${s}_{i}$ for an element of ${S}_{i}$ and ${\sigma}_{i}$ for an element of ${\mathrm{\Sigma}}_{i}$.
Title  strategy 

Canonical name  Strategy 
Date of creation  20130322 12:52:02 
Last modified on  20130322 12:52:02 
Owner  Henry (455) 
Last modified by  Henry (455) 
Numerical id  7 
Author  Henry (455) 
Entry type  Definition 
Classification  msc 91A99 
Related topic  Game 
Defines  strategy 
Defines  pure strategy 
Defines  mixed strategy 
Defines  strategy space 