COMP34120
Two hours
UNIVERSITY OF MANCHESTER
SCHOOL OF COMPUTER SCIENCE
AI and Games
Date: Tuesday 7th June 2016
Time: 14:00 - 16:00
Please answer any THREE Questions from the FOUR Questions provided
Use a SEPARATE answerbook for each QUESTION
This is a CLOSED book examination
The use of electronic calculators is NOT permitted
[PTO]
, COMP34120
1. a) If it is announced that the (7, 7) Kalah is solved, give 3 things that this could
possibly mean. (3 marks)
b) The following is a two-player, zero-sum game in normal form.
Alice
A B C D
a 4 3 2 5
Bob b 3 2 1 4
c 2 1 0 3
i) Find the equilibrium of this game using the minimax approach. (3 marks)
ii) Find the equilibrium of this game using another approach. (2 marks)
c) The figure below shows a game tree for a two-player, zero-sum game. The square
nodes are the MAX player and the round nodes are the MIN player. Terminal nodes
are labelled by their outcomes, which is a value.
R
1 2
*
1.1 1.2 2.1 2.2
♠
1.1.1 1.1.2 1.2.1 1.2.2 2.1.1 2.1.2 2.2.1 2.2.2
10 11 9 12 14 15 13 14 5 2 4 1 3 22 20 21
i) What is the value of the root node? Justify your answer. (2 marks)
ii) What branches of the subtree do not have to be evaluated? Assume that child
nodes are evaluated from left to right.
To label a branch, list the parent of that branch and the direction of the child:
‘Left’ or ‘Right’. For example, the branch marked with the asterisk (∗) would
be 2 ’Right’ which would eliminate 2.2, 2.2.1. and 2.2.2. The branch marked
with the spade symbol (♠) would be 2.1 ’Left’, which would eliminate 2.1.1.
(5 marks)
Page 2 of 6
Two hours
UNIVERSITY OF MANCHESTER
SCHOOL OF COMPUTER SCIENCE
AI and Games
Date: Tuesday 7th June 2016
Time: 14:00 - 16:00
Please answer any THREE Questions from the FOUR Questions provided
Use a SEPARATE answerbook for each QUESTION
This is a CLOSED book examination
The use of electronic calculators is NOT permitted
[PTO]
, COMP34120
1. a) If it is announced that the (7, 7) Kalah is solved, give 3 things that this could
possibly mean. (3 marks)
b) The following is a two-player, zero-sum game in normal form.
Alice
A B C D
a 4 3 2 5
Bob b 3 2 1 4
c 2 1 0 3
i) Find the equilibrium of this game using the minimax approach. (3 marks)
ii) Find the equilibrium of this game using another approach. (2 marks)
c) The figure below shows a game tree for a two-player, zero-sum game. The square
nodes are the MAX player and the round nodes are the MIN player. Terminal nodes
are labelled by their outcomes, which is a value.
R
1 2
*
1.1 1.2 2.1 2.2
♠
1.1.1 1.1.2 1.2.1 1.2.2 2.1.1 2.1.2 2.2.1 2.2.2
10 11 9 12 14 15 13 14 5 2 4 1 3 22 20 21
i) What is the value of the root node? Justify your answer. (2 marks)
ii) What branches of the subtree do not have to be evaluated? Assume that child
nodes are evaluated from left to right.
To label a branch, list the parent of that branch and the direction of the child:
‘Left’ or ‘Right’. For example, the branch marked with the asterisk (∗) would
be 2 ’Right’ which would eliminate 2.2, 2.2.1. and 2.2.2. The branch marked
with the spade symbol (♠) would be 2.1 ’Left’, which would eliminate 2.1.1.
(5 marks)
Page 2 of 6
