Romeo composes a letter to Juliet, and gives it to Tybalt to deliver to Juliet. While on the way, Tybalt peeks at the letter's contents. Tybalt gives Juliet the letter, and Juliet reads it immediately, in Tybalt's presence. Neither Romeo nor Juliet knows that Tybalt has read the letter.
Answer the following questions relating to this story:
(a) Construct an Aumann model of incomplete information in which all the elements of the story above regarding the knowledge possessed by Romeo, Tybalt, and Juliet regarding the content of the letter hold true (there are several possible ways to do this). Specify a state of the world in the model that corresponds to the situation described above.
(b) In the state of the world you specified above, does Romeo know that Juliet has read the letter? Justify your answer.
(c) In the state of the world you specified above, does Tybalt know that Romeo knows that Juliet has read the letter? Justify your answer.
(d) Construct an Aumann model of incomplete information in which, in addition to the particulars of the story presented above, the following also holds: "Tybalt does not know that Juliet does not know that Tybalt read the letter," and specify a state of the world in your model that corresponds to this situation.