A strictly dominated strategy can be defined as follows -

1.For player i, a pure strategy si Si is strictly dominated by a mixed strategy

i (Si) if ui(i , si) > ui(si , si) for all si Si (1)

Prove that this definition is equivalent to the following definition.

2.For player i, a pure strategy si Si is strictly dominated by a mixed strategy

i (Si) if ui(i , i) > ui(si , i) for all i Si (2)

In other words, show (1) implies (2) and (2) implies (1).