Assignment:
Construct an Aumann model of incomplete information for each of the following situations, and specify a state of the world in that model which corresponds to the situation (there are several possible ways of including higher-order beliefs in each model):
(a) Mary gave birth to a baby, and Herod knows it.
(b) Mary gave birth to a baby, and Herod does not know it.
(c) Mary gave birth to a baby, Herod knows it, and Mary knows that Herod knows it.
(d) Mary gave birth to a baby, Herod knows it, but Mary does not know that Herod knows it.
(e) Mary gave birth to a baby, Herod does not know it, and Mary does not know whether Herod knows it or not.
Provide complete and step by step solution for the question and show calculations and use formulas.