Use example sheet for 1 and 2! Game Theory! Example images:

1. Determine which player has a winning strategy in the following game of Tape Dominoes: Justify your answer. 2. Find a winning move (if any) for the following Tape Dominos position. Justify your answer. W Example. Find winning moves (if any) for the following Tape Dominos positions ( a) Since the Grundy Number of this position is by = 170 this is a positive position. Thus, there is a winning move Blank tape w/ 5 cells This position has Grundy number by = 0 and is thus a zero position corresponds corres ponds to pile with 2 to pile with 1 corresponds to pile objects . object with O objects ( b ) Grundy number of this WINNING move ! position is b 2 by O 2 ASIDE = 2 + 21 2/0 12 = 3 70 This this is a positive position and there is a winning move . ( corresponds to removing 21- 20= 2-1=1 object from pile with 2 objects in a game of Nim, so we must place domino on that Comesponding Piece of tape )