Due Tuesday, August 16th, 11:59 pm EST via Moodle. (100 pts total) (Please show all math work and reasoning for your answers; impartial work will not be graded fully) 1) Consider the following 2-player, simultaneous, single-shot game, where Pl has the options to choose up, middle, or down (U, M, D); P2 has the options to choose apples, bananas, or cherries (A, B, C). The payouts for each strategy: (U,A) = (12,4); (U,B) = (4,3); (U,C) = (8,8); (M,A) = (10,7); (M,B) = (5,4); (M,C) = (3,6); (D,A) = (13,8); (D,B) = (5,6); & (D,C) = (1,7). (25 pts) a. Draw this game in standard form (5 pts). b. Given the known payouts, identify all possible Nash Equilibriums (10 pts). [Hint: you may need to eliminate possible strategies] c. What are the optimal strategies for each player given a mixed equilibrium (10 pts)? EC: Generally, is there any motivation from any Player to move from a Nash Equilibrium (3 pts)