reflect on a

Students in ECO 405 can answer either Question 5a or Question 5b but not both. Students in ECO 505 must answer Question 5b but not 5a. 53. (10 points) Reect on an idea that you have learned from this course and describe how it might be related to some real world experience. [120 nerds maximum) 5!). (10 points) Consider a. variant of the game Nim, which we played in class. Recall that the rules of the game are the following: i. Two players take turns to remove matches from several piles. ii. Each player, when it is his turn to move, can remove any number of matches (at least one and up to the entire pile) from any pile but not from multiple piles. iii. The player who removes the last match wins. We know that if there are only M piles and bath piles have the same number of matches, for example, (2, 2), then the player who moves in the second place has a winning strategy, i.e. he is guaranteed to remove the last match. In the winning strategy the second mover simply mimics the rst-mower: each time Player 1 takes some matches from a pile Player 2 takes the same number of matches from the other pile. For each of the following cases, use the above result and apply the thinking of backward induction to nd out who has a winning strategy and describe the winning strategy in details: (1) (3pts) three piles (10, 10, 10) {ii} {7pm} three piles (3, 2, 1)