Let A be a real 3 x 2 matrix, and let Γ be the mixed extension of the bimatrix game whose payoffs are described by A for the row player and B for the column player.
1. If A = [insert matrix here], then find the mixture of the first and second row that strictly dominates the third row. Also, find the unique Nash equilibrium of Γ.
2. Let A = [insert matrix here]. Demonstrate that if the column player selects a mixed strategy such that the row player is indifferent between the first and second row, then he strictly prefers the third row. Moreover, find all Nash equilibria.
(The strategy of the row player in each Nash equilibrium is uniquely determined and pure, and the column player has a continuum of equilibrium strategies and none of them is pure.)