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Simfish

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## Main Question or Discussion Point

Quote: "Let [tex]G = <N, (A_i), (u_i)> [/tex] be such a strategic game. We denote by [tex]\Delta (A_i )[/tex] the set of probability distributions over [tex]A_i[/tex] and refer to a member of [tex]\Delta (A_i )[/tex] as a mixed strategy of player i; we assume that the players' mixed strategies are independent randomizations. "

So notationally there is a difference between pure and mixed strategies; however, how does this translate to a physical difference between a pure and a mixed strategy? Where does the Delta notation come from? (I'm reading a really abstract book on game theory)

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EDIT:

From http://www.virtualperfection.com/gametheory/1.StrategicFormGames.1.0.pdf ,

When A is a finite set, [tex]\Delta (A_i )[/tex] is the set of all probability distributions over A. So how then, would we list the set of all probability distributions over A? Is the set infinite? (because you can assign any probability from [0,1] to the elements of A, and the range of the set has an infinite number of elements)

So notationally there is a difference between pure and mixed strategies; however, how does this translate to a physical difference between a pure and a mixed strategy? Where does the Delta notation come from? (I'm reading a really abstract book on game theory)

===

EDIT:

From http://www.virtualperfection.com/gametheory/1.StrategicFormGames.1.0.pdf ,

When A is a finite set, [tex]\Delta (A_i )[/tex] is the set of all probability distributions over A. So how then, would we list the set of all probability distributions over A? Is the set infinite? (because you can assign any probability from [0,1] to the elements of A, and the range of the set has an infinite number of elements)

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