This document provides an overview of game theory concepts. It begins by listing the key learning objectives, which include understanding the importance of game theory in decision making, analyzing pure and mixed strategy games, and using dominance to simplify games. The document then covers various game theory topics like the minimax criterion, Nash equilibrium, prisoner's dilemma examples, and how to solve mixed strategy games. Examples are provided to illustrate pure strategy, mixed strategy, and dominance concepts. The summary concludes by mentioning further reading materials on quantitative methods and game theory.

1. BBA3274 / DBS1084 QUANTITATIVE METHODS for BUSINESS
Game Theory
Game Theory
by
Stephen Ong
Visiting Fellow, Birmingham City
University Business School, UK
Visiting Professor, Shenzhen

2. Today’s Overview

3. Learning Objectives
After this lecture, students will be able to:
1.
2.
3.
4.
Understand the importance and use
of game theory in decision making.
Understand the principles of zerosum, two person games.
Analyse pure strategy games and
use dominance to reduce the size of
the game.
Solve mixed strategy games when
there is no saddle point.

4. Outline
4.1
4.2
4.3
4.4
4.5
4.6
Introduction
Language of Games
The Minimax Criterion
Pure Strategy Games
Mixed Strategy Games
Dominance

5. Game Theory Models

5
A set of mathematical tools for
analyzing situations in which players
make various strategic moves and have
different outcomes or payoffs
associated with those moves.

6. Dominant Strategies and the
Prisoner’s Dilemma

6
This payoff matrix
shows the various
prison terms for Bonnie
and Clyde that would
result from the
combination of
strategies chosen when
questioned about a
crime spree.

7. Prisoner’s Dilemma –
Dominant Strategy

7
A dominant strategy
is one that results in
the best outcome or
highest payoff to a
given player no
matter what action
or choice the other
player makes.

8. Nash Equilibrium

8
Nash equilibrium is
a set of strategies
from which all
players are
choosing their best
strategy, given the
actions of the other
players.

9. Game Model Classification
 Number
of
players
 Sum of all
payoffs
 Number of
strategies
employed
 Two
person
(X, Y)
 Zero sum,
where sum of losses
by one player = sum
of gains by other
player

10. Example : Duopoly of 2 Stores




10
There are only 2
lighting fixture stores, X
and Y.
Owner of store X has 2
advertising strategies –
radio spots and
newspaper ads.
Owner of store Y
prepares to respond
with radio spots and
newspaper ads.
The 2x2 payoff matrix
shows the effect on
market shares when
both stores advertise.

11. Example : Duopoly Game
Outcomes
Store X
Strategy
Store Y
Strategy
Outcome
(% Change in Market
Share)
X1
(Use Radio)
Y1
(Use Radio)
X wins 3
And Y loses 3
X1
(Use Radio)
Y2
(Use Newspaper)
X wins 5
And Y loses 5
X2
(Use Newspaper)
Y1
(Use Radio)
X wins 1
And Y loses 1
X2
(Use Newspaper)
Y2
(Use Newspaper)
X loses 2
And Y wins 2
1- 11

12. Minimax Criterion
Used to find the strategy that minimises
the maximum loss, or maximizes the
minimum payoff (maximin approach).
 Locate the minimum payoff for each strategy.
 Select the strategy with the maximum number.
 The upper value of the game equal to the
minimum of the maximum values in the
columns.
 The lower value of the game is equal to the
maximum of the minimum values in the rows.
3-12

13. Minimax Solution
An equilibrium or saddle point condition exists if the
upper value of the game is equal to the lower value of
the game. This is called the value of the game.
Saddle Point
STRATEGIES
X1
Y1
3
Y2
5
X2
1
-2
MAXIMUM
3
5
Minimum of maximums
MINIMUM
3
-2
Maximum of minimums
3-13

14. Pure Strategy Game
When a saddle point is present, the strategy each
player should follow will always be the same
regardless of the other player’s strategy.
Saddle Point
STRATEGIES
X1
Y1
10
Y2
6
X2
-12
2
MAXIMUM
10
6
Minimum of maximums
MINIMUM
6
-12
Maximum of minimums
3-14

15. Mixed Strategy Game
When there is no saddle point, players will play each
strategy for a certain percentage of the time (P, Q).
To solve a mixed strategy game, use the expected
gain or loss approach.
STRATEGIES
Y1
(P)
Y2
(1 - P)
Expected
Gain
X1 (Q)
4
2
4P + 2(1-P)
X2 (1 - Q)
1
10
1P + 10(1-P)
Expected
gain
4Q + 1(1-Q) 2Q + 10(1-Q)
3-15

16. Mixed Strategy Game
The goal of this approach is for a player to play each
strategy a particular percentage of the time so that
the expected value of the game does not depend
upon what the opponent does. This will only occur if
the expected value of each strategy is the same.
For player Y,
4P + 2 (1 – P) = 1P + 10(1 – P)
P = 8/11
For player X,
4Q + 1(1 – Q) = 2Q + 10(1 – Q)
Q = 9/11
3-16

17. Dominance


17
The principle of
dominance can be used
to reduce the size of the
games by eliminating
strategies that would
never be played.
A strategy can be
eliminated if all its
game’s outcomes are
the same or worse than
the corresponding
game outcomes of
another strategy.

18. Example : Dominance
Y1
Y2
Y3
Y4
X1
-5
4
6
-3
X2
-2
6
2
-20
1- 18

19. Tutorial
Lab Practical : Spreadsheet
1 - 19

20. Further Reading



Render, B., Stair Jr.,R.M. & Hanna, M.E.
(2013) Quantitative Analysis for
Management, Pearson, 11th Edition
Waters, Donald (2007) Quantitative
Methods for Business, Prentice Hall, 4 th
Edition.
Anderson D, Sweeney D, & Williams T.
(2006) Quantitative Methods For
Business Thompson Higher Education,
10th Ed.

21. QUESTIONS?