G1 := RandDisGame(4, 4): G2 := RandDisGame(5, 7): print(Matrix(G1)): print(Matrix(G2)): # G1:= [8,10] [9,11] [6,15] [1,16] # [5,13] [10,14] [16,12] [4,5] # [14,9] [15,4] [11,1] [2,8] # [13,2] [7,7] [12,3] [3,6] # G2:= [9,16] [21,19] [14,13] [24,32] [25,10] [17,5] [7,12] # [30,35] [2,23] [34,28] [19,3] [8,17] [4,8] [23,14] # [3,24] [29,6] [18,18] [12,34] [20,9] [1,30] [27,2] # [5,33] [31,31] [16,20] [13,11] [15,25] [6,1] [10,7] # [28,27] [22,26] [11,21] [32,29] [26,15] [35,4] [33,22] #(a) Using G1: # (i) find the outcome of the sequential version of G1 when Player Row goes first # Option 1: Row chooses strategy R1, Column responds with strategy C4 for an outcome of 1-16 # Option 2: Row chooses strategy R2, Column responds with strategy C2 for an outcome of 10-14 # Option 3: Row chooses strategy R3, Column responds with strategy C1 for an outcome of 14-9 # Option 4: Row chooses strategy R4, Column responds with strategy C2 for an outcome of 7-7 # So Row chooses strategy R3 which maximizes Row's points, and row wins with strategy [3,1] and outcome [14,9] # (ii) find the outcome of the sequential version of G1 when Player Column goes first # Option 1: Column chooses strategy C1, Row responds with strategy R3 for an outcome of 14-9 # Option 2: Column chooses strategy C2, Row responds with strategy R3 for an outcome of 15-4 # Option 3: Column chooses strategy C3, Row responds with strategy R2 for an outcome of 16-12 # Option 4: Column chooses strategy C4, Row responds with strategy R2 for an outcome of 4-5 # So Column chooses strategy C3 which maximizes Column's points, but row wins with strategy [2,3] and outcome [16,12] Here a better strategy for C would be C4, this is the only choice in which column wins. Further, maximizing the differences {9-14, 4-15, 12-16, 5-4} = {-5, -11, -4, 1} would give us this strategy!