For a non-cooperative bimatrix game the feasible set is
$$\{(u,v)=(\mathbf{p}^TA \mathbf{q},\mathbf{p}^TB \mathbf{q}):p \in X^*, q \in Y^*\}$$
graph the non-cooperative feasible set for the Battle of the Sexes with bimatrix,
$$\left(\begin{array}{cccc}(2,1)&(0,0)\\(0,0)&(1,2)\end{array}\right)$$
My thoughts:
When I calculated $\mathbf{p}^T A \mathbf{q}$ I get $3pq-p-q+1$.. If I set this equal to 0 the graph is a hyperbola. It is similar for $\mathbf{p}^T B \mathbf{q}$.. However, I don't think I am on the right track, and not really sure the interpretation. Game theory is still quite new to me. Appreciate any help!
Plot the payoff profiles (2,1), (0,0) and (1,2) in two-dimensional payoff space. The convex hull of these points is the set of feasible payoffs under (correlated) mixed strategies.