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Lecture 4
Game Theory
Source:
/1
/
D.R.Anderson, D.J.Sweeney, T.A.Williams. Quantitative Methods for Business, South
Western College Publishing, 11th edition.
Chapter 5.
Contents:
4.1
Introduction to Game Theory
4.2
Mixed Strategy games
4.1 Introduction to Game Theory
In decision analysis, a single decision maker seeks to select an optimal decision
alternative after considering the possible outcomes of one or more chance events. In game
theory, two or more decision makers are called players, and they compete as adversaries
against each other. Each player selects a strategy independently without knowing in advance
the strategy of the other player or players. The combination of the competing strategies
provides the value of the game to the players. Game theory applications have been developed
for situations in which the competing players are teams, companies, political candidates,
armies, and contract bidders.
In this section, we describe
twoperson, zerosum games
.
Twoperson
means that two
competing players take part in the game.
Zerosum
means that the gain (or loss) for one player
is equal to the corresponding loss (gain) for the other player. As a result, the gain and loss
balance out so that the game results in the sum of zero. What one player wins, the other player
loses. Let us demonstrate a twoperson, zerosum game and its solution by considering two
companies competing for market share.
Example 4.1.
Competing for Market Share
Suppose that two companies are the only manufacturers of a particular product; they
compete against each other for market share. In planning a marketing strategy for the coming
year, each company is considering three strategies designed to take market share from the other
company. The three strategies, assumed to be the same for both companies, are as follows:
Strategy 1
Increase advertising
Strategy 2
Provide quantity discounts
Strategy 3
Extend product warranty
A payoff table showing the percentage gain in the market share for Company A expected for
each combination of strategies follows. The notations
a
1 ,
a
2
,
and
a
3
identify the three strategies
for Company A; the notations
b
1
,b
2
,
and
b
3
identify the three strategies for Company B. It is a
zerosum game because any gain in market share for Company A is a loss in market share for
Company B.
Company B
Increase
Advertising
b
1
Quantity
Discounts
b
2
Extend
Warranty
b
3
Company A
Increase Advertising,
a
1
4
3
2
Quantity Discounts,
a
2
1
4
1
Extend Warranty,
a
3
5
2
0
1
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View Full DocumentIn interpreting the entries in the table we see that if Company A increases advertising (
a
1
)
and Company В increases advertising (
b
1
), Company A will come out ahead with an increase
in market share of 4%. On the other hand, if Company A provides quantity discounts (
a
2
) and
Company В increases advertising (
b
1
), Company A is projected to lose 1% of market share to
Company B. Company A is seeking payoff values that show relatively large increases in its
market share. Company В is seeking payoff values that show decreases or small increases in
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 Spring '11
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 Game Theory

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