Let = be a decision problem for {1 2}. Compare the two decision problems 1 and

Let Δ =

¡

   

¢

be a decision problem for  ∈ {1 2}.

Compare the two decision problems Δ1 and Δ2 given by

1 = { }

 1 = { }

1 ( ) = 1 ( ) = 1

1 ( ) = 1 ( ) = 0 If  ∈ Σ is rationalizable with respect to , then  is rationalizable with respect to Ω

Let Δ = ¡
   
¢