Assignment:
What is the set of possible payoffs of the following game (the Battle of the Sexes game) if:
(a) the players are permitted to decide, and commit to, the mixed strategies that each player will use;
(b) the players are permitted to make use of a public lottery that chooses a strategy vector and instructs each player which pure strategy to choose.
Provide complete and step by step solution for the question and show calculations and use formulas.