- Consider A Simple Two Player Game With Only Two Possible Moves For Each Player L Left And R Right First Player 1 M 1 (113.86 KiB) Viewed 21 times
Consider a simple two-player game with only two possible moves for each player, L (left) and R (right). First player 1 makes a move, then player 2 makes a move and then player 1 makes a move again. After this the game ends. We denote each possible game by the sequence of moves made, e.g. (L, R, L) is the game where player 1 initially chooses L, then player 2 chooses R, and player 1 finally also chooses L again. Below is listed the outcome of each possible game: (L, L, L): it is a tie (L, L, R): player 1 loses (L, R, L): player 1 loses 2 (L, R, R): player 1 loses (R, L, L): player 1 wins (R, L, R): player 1 loses (R, R, L): it is a tie ● (R, R, R): player 1 loses. We define the utility function to have value 1 for the winner of the game, -1 for the loser, and 0 if it is a tie. a. Draw the game tree of the game and add the minimax values to all nodes. b. Is it a zero-sum game? Explain your answer. c. Will player 1 win, lose or get a tie, assuming that both players play optimally (according to the Minimax algorithm)? Explain your answer. d. Which game will be played when both players play optimally, that is, what is the sequence of moves made? e. Is it possible to guarantee player 1 a win by changing a single of the game outcomes in the list above? If no, then why not? If yes, list each game outcome that would turn the game into a win for player 1, and explain why. ● ● ● ●