In the course content, it is explained how to solve two-player zero-sum games using linear pro- gramming. One of the games described is "Rock-Paper-Scissors." In this problem the game is examined closer. Assume the the following is a "loss" matrix for Player 1, e.g., the matrix shows how much Player 1 has lost rather than gained so the sign is reversed: 01-1 -1 0 (a) What is the expected loss for Player 1 when Player 1 plays a mixed strategy x(r 2,s) and Player 2 plays a mixed strategy y-(yi,Y2,U3)? (b) Show that Player 1 can achieve a negative expected los i.e., an expected gain) if Player 2 plays amy strategy other than y = (yi,Y2, ) = (, , (c) Show that xnd y r Nash equilibrium (d) Let x-( , , ) as in part (c). Is it possible for (x, y) to be a Nash equilibrium for sone mixed strategy y'( ? Explain. 3 3' 3