(a) Consider an alternative definition of iterated strict dominance that proceeds as in section…

(a) Consider an alternative definition of iterated strict dominance that proceeds as in section 2.1 except that, at each state n, only the strictly dominated pure strategies of players I(n) ⊆ I are deleted. Suppose that, for each player I, there exists an infinite number of steps n such that I ϵ I(n). If the game is finite, show that the resulting limit set is S∞ (as given in definition 2.1), so that there is no loss of generality in taking I(n) = I for all n. Hint: The intuition is that if a strategy si is strictly dominated at step n but is not eliminated because i ∉ I(n), then it will be eliminated at the next step n’> n such that i ∈ I(n’), as (i) the set of strategies s-i remaining at step n’ is no larger than the set of strategies s-i  remaining at step n and

(ii) if