MATHEMATICS
P.4
Game Theory
The mathematics hidden within oligopolistic markets
Kade Stroude
This
What is Game Theory?
Game theory in its essence is the science behind
human strategy and human interactions. It briefly
attempts
to
address
behavioural
economics,
mathematics and psychology as to explain how humans
use economics to predict another’s thought processes
in a battle of wits.
can be explained using game theory:
Assume Pepsi advertise moderately. You expect Coca
Cola will act similarly, and thus expected profits are
£120m. However what if Coca Cola advertise heavily?
The new expected profit is reduced to £25m, £95m less
than before.
Table 1
The Invisible Hand
Adam Smith, arguably the most influential economist of
all time, suggested that if people were to act in selfinterest, it would benefit society as a whole. This
phenomenon would be known as the invisible hand.
However this is not always the case, according to game
theory, when any two (or more) parties are given a
choice in which interdependence occurs, self-interest
may prevent the most profitable outcome.
How does this relate to economics?
An example of this is Coca Cola and Pepsi branded
soda. Most people are aware of such household names,
whether they purchase the products or not, and this is
due to large advertisement. In 2010 alone Coca Cola
spent $2.9 billion on advertisement worldwide, more
than Microsoft and Apple Inc. combined!
Large firms who operate in a highly competitive market
do not like the possibility of the worst scenario outcome,
therefore by advertising heavily they would only receive
£70 million less in profits (£120m - £50m), which is
significantly less than the previous scenario.
This same ideology suggests the reason for collusion
(When firms join together to undertake a joint decision
i.e. price setting, quantity of goods supplied in a
markets). For firms to reach an optimal outcome they
have to work together - this logical progression is
caused by the impossibility to second-guess an
opponent’s choice.
Table 2
However we must ask ourselves why?
Game theory suggests an explanation exogenous to
Adam Smith’s invisible hand. Coca Cola and Pepsi
spend so much on advertising because their
competitors spend so much on advertising - they must
both in order to maintain a market share.
Here it is likely that as the firms act in self-interest, they
will lower prices to increase their individual revenue,
meaning that in actuality will both lose revenue [Table
2]. Therefore it is argued that collusion will allow for both
firms to maintain revenues as market uncertainty is
erased. This is called a tacit collusion. Nonetheless
collusion is illegal, because the exploitation of
consumers is looked down upon.