AI Applications in ECE

Problem Set $($Total $100$ points$)$

Q$1.$ Consider a simple zero$-$sum game where two players take turns choosing numbers from a list $[5,3,7,10].[10$pts$]$

Players can pick only the first or the last number from the list.

Player $1($Maximizer$)$ tries to maximize their score, while Player $2($Minimizer$)$ tries to minimize Player $1\text{'}$s score.

Both players play optimally.

Use the Minimax algorithm to calculate the optimal strategy for Player $1$ and determine the scores. Include the game tree and calculate the Minimax values for intermediate nodes.

Start point is given:

Represent the Problem as a Game Tree

At each step, the game tree branches based on whether the players pick the first or last number from the list. Below is the tree for the game $5,3,7,10$ :

Level $0$: $5,3,7,10($Player $1-$ Max$)$

$[3,7,10],[5,3,7]$

$($Player $2-$ Min$)($Player $2-$ Min$)$

$[7,10][3,7][3,7][5,3]$

$($Player $1-$ Max$)($Player $1-$ Max$)$

$[10][7][7][3][7][3][3][5]$