I need ten words but I need hellp for this q

Consider the Matching Pennies game below. H T H 1, -1 -1, 1 T -1, 1 1, -1 Let > denote the set of mixed strategy profiles for this game. (a) Consider a mapping f : E - > such that ((1/2, 1/2), (1/2, 1/2)) if ((p, 1 - p), (q, 1 - q)) = ((1/2, 1/2), (1/2, 1/2)) f((p, 1-p), (q, 1-q)) = or if ((p, 1 - p), (q, 1 - q)) = ((1, 0), (0, 1)), ( ((1,0), (0, 1)) otherwise. Show that a strategy profile o is a fixed point of f if and only if o is a mixed strategy equilibrium of the Matching Pennies game. (b) Argue that f does not satisfy the conditions of Brouwer's fixed point theorem. (c) Consider a mapping g : E - > such that g(o) = ((1/4, 3/4), (1/2, 1/2) ) for all o E E. Argue that g satisfies the conditions of Brouwer's fixed point theorem, and find the fixed points of g. (d) Show that none of the strategy profiles that are fixed point of g are also mixed strategy equilibria of the Matching Pennies game