Show that in the coinsinaline game a greedydenial strategy o

Show that, in the coins-in-a-line game, a greedy-denial strategy of having the first player, Alice, always choose the available coin that minimizes the maximum value of the coin available to Bob will not necessarily result in an optimal solution for her.

Solution

Solution:

                                             In the game 100,101,100,1

if Alice plays according to the greedy-denial strategy, she will choose 1 (to deny Bob coin101), then Bob will choose 100, so Alice will have a value of 102, whereas Bob will havea value of 200. On the other hand, if Alice plays optimally, she will choose 100 rst, and Bob will choose 101 (if he plays optimally). Alice will earn 200 and Bob 102. This showsthat the greedy-denial strategy is not always optimal.

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