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 distributionPlanetmathPlanetmath 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:

  • Si for the strategy space of the i-th player

  • si for a particular element of Si; that is, a particular pure strategy

  • σi for a mixed strategy. Note that σiSi[0,1] and siSiσi(si)=1.

  • Σi for the set of all possible mixed strategies for the i-th player

  • S for iSi, the set of all possible of pure strategies (essentially the possible outcomes of the game)

  • Σ for iΣi

  • σ for a strategy profile, a single element of Σ

  • S-i for jiSj and Σ-i for jiΣj, the sets of possible pure and mixed strategies for all players other than i.

  • s-i for an element of S-i and σ-i for an element of Σ-i.

Title strategy
Canonical name Strategy
Date of creation 2013-03-22 12:52:02
Last modified on 2013-03-22 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