Question

24. The game called “Nim” goes like this: there are a pile of five stones on the ground. Player 1 can take either 1 or 2 stones. Then player 2 can take either 1 or 2 stones. They continue taking either 1 or 2 stones in turn until all the stones are gone. The player who takes the last stone (or stones) wins. a. Model this as an extensive form game and find the subgame perfect Nash equilibria. b. What happens when you start with n stones instead of five?

Answer 1

if stones are 5 should considered then player 1 choose 2 stones at the begining round . In 2nd round player 2 would choose either SINE 1 ar 2 chooses ; If pl.2 stones, 1 stone then plet can win game by choosing remaining 2 Stones or if pl.1 chooses a stones then pl. 1 can win game by choosing last ston Re. 1 - 1 t round Rel² stones - 2nd round Pl.1 – 3 round, stones stones ® when When we then we assume will solve that we have this game by unll stones assuming Whether na even OR na odd.

let, consider, are at we last stage of game where we will win this game by choosing 1 w 2 stones can .. such situation will anix when you would pick up (n-3rd stone because after that irrespective of choice made to other player (1 as a stones) you can surely win game in last round. similarly if you go back we have to mok sure that you pick up B ak)th store in each kth round, rets assume if n is even then 4 na sol I then we choose 47th, 44th, ... era, stone & n = 5 then we choose 48th, 45th - choose 2 stong 3rd se at then if begining iz play and n is even round n is odd as chances then choose atstone to of choosing 3rd stone in round a ise
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