midterm1_solutions.pdf - Solutions to Problems from Midterm 1 Stat 155 Game Theory(Fall 2017 Soumendu Sundar Mukherjee Note If you have comments or

# midterm1_solutions.pdf - Solutions to Problems from Midterm...

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Solutions to Problems from Midterm 1 Stat 155, Game Theory (Fall 2017) Soumendu Sundar Mukherjee Note: If you have comments or questions about the solutions, feel free to email me at [email protected] . Question 1Consider a game ofsubtractionbetween two players: there is a pile ofxchips wherexis a positive integer. Each player,on his turn, must remove a numbernof chips wheren∈ {1,4,5}. The player who removes the last chip wins. Is thepositionx= 12 aP-position (winning position for previous player) orN-position (winning position for next player)?Explain your answer. Question 2Consider a game ofNimwith three heaps of sizes 6, 7, and 8. Each player, on his turn, must remove a positive number ofchips from a single heap. The player who removes the last chip wins.a. (6,7,8) is anN-position (winning position for next player) in this game: explain why.b. Describe the first move in a winning strategy for the next player.