Game Theory
Game theory is mainly concerned with predicting the outcome of games of strategy in which the participants (for example
two or more businesses competing in a market) have incomplete informationabout the others' intentions.
Game theory analysis has direct relevance to the study of the conduct and behaviour of firms in oligopolistic markets – for
example the decisions that firms must take over pricing and levels of production,
and also how much money to invest in research and development spending.
Costly research projects represent a risk for any business – but if one firm invests in R&D, can a rival firm
decide not to follow? They might lose the competitive edge in the market and
suffer a long term decline in market share and profitability.
The dominant strategy for both firms is probably to go ahead with
R&D spending. If they do not and the other firm does, then their profits
fall and they lose market share. However, there are only a limited number of
patents available to be won and if all of the leading firms in a market spend
heavily on R&D, this may ultimately yield a lower total rate of return than
if only one firm opts to proceed.
The Prisoners’
Dilemma
 The
classic example of game theory is
the Prisoners’ Dilemma, a situation where two prisoners are being
questioned over their guilt or innocence of a crime.
 They
have a simple choice, either to confess to the crime (thereby implicating
their accomplice) and accept the consequences, or to deny all involvement
and hope that their partner does likewise.
Confess or keep quiet? The Prisoner’s
Dilemma is a classic example of basic game theory in action!
 The
“payoff” is measured in terms of years in prison arising from their
choices and this is summarised in the table below.
 No
communication is permitted between the two suspects – in other words, each
must make an independent decision, but clearly they will take into account
the likely behaviour of
the other when underinterrogation.
Nash Equilibrium A Nash Equilibrium is an idea in game theory – it describes any
situation where all of the participants in a game are pursuing their best
possible strategy given the strategies of all of the other participants. In a Nash Equilibrium, the outcome of a game that occurs is when player
A takes the best possible action given the action of player B, and player B
takes the best possible action given the action of player A.
Two prisoners are held in a separate room and cannot communicate They are both suspected of a crime They can either confess or they can deny the crime Payoffs shown in the matrix are years in prison from their chosen
course of action

Prisoner A


Confess

Deny


Prisoner B

Confess

(3 years, 3 years)

(1 year, 10 years)

Deny

(10 years, 1 year)

(2 years, 2 years)

 What
is the best strategy for
each prisoner? Equilibrium happens when each player takes decisions which
maximise the outcome for them given the actions of the other player in the
game.
 In
our example of the Prisoners’ Dilemma, the dominant
strategy for
each player is to confess since this is a course of action likely to
minimise the average number of years they might expect to remain in
prison.
 But
if both prisoners choose to confess, their “payoff” i.e. 3 years each in
prison is higher than if they both choose to deny any involvement in the
crime.
 In
following narrowly defined selfinterest, both prisoners make themselves
worse off
 That
said, even if both prisoners chose to deny the crime (and indeed could
communicate to agree this course of action), then each prisoner has an incentive
to cheat on
any agreement and confess, thereby reducing their own spell in custody.
The equilibrium in the Prisoners’ Dilemma occurs when each player
takes the best possible action for themselves given the action of the other player.
The dominant strategy is each prisoners’ unique best strategy regardless of the other players’ action Best strategy? Confess?
A bad outcome! – Both prisoners could do better by both denying – but
once collusion sets in, each prisoner has an incentive to cheat!

Prisoner A


Confess

Deny


Prisoner B

Confess

(3 years, 3 years)

(1 year, 10 years)

Deny

(10 years, 1 year)

(2 years, 2 years)

Applying the
Prisoner’s Dilemma to business decisions
 Game theory examples
revolve around the payoffs that
come from making different decisions.
 In
the classic prisoner’s dilemma the reward
to defecting is greater than mutual cooperation which
itself brings a higher reward than mutual defection which itself is better
than the sucker’s payoff.
 Critically,
the reward for two
players cooperating with each other is higher
than the average reward from defection and the sucker’s payoff.
Consider this example of a simple pricing game: The values in the table
refer to the profits that flow from making a particular decision.

company B’s output


High output

Low output


Company A’s output

High output

Rs. 5m, Rs.5m

Rs.12m, Rs.4m

Low output

Rs.4m, Rs.12m

Rs.10m, Rs.10m

 Display
of payoffs: row first, column second e.g. if Firm A chooses a high output
and Firm B opts for a low output, company A wins Rs.12m and company B wins
Rs. 4m.
 In
this game the reward to both firms choosing to limit supply and thereby
keep the price relatively high is that they each earn Rs. 10m. But
choosing to defect from this strategy and increase output can cause a rise
in market supply, lower prices and lower profits – Rs. 5m each if both
choose to do so.
A dominant strategy is a strategy that
is best irrespective of the other player’s choice. In this case the dominant
strategy is competition between the firms.
 The Prisoners’
Dilemma can
help to explain the breakdown of pricefixing agreements between producers
which can lead to the outbreak of price wars among suppliers, the
breakdown of other joint ventures between
producers and also the collapse of freetrade agreements between countries
when one or more countries decides that protectionist strategies are in
their own best interest.
 The
key point is that game theory provides an insight into the interdependent
decisionmaking that
lies at the heart of the interaction between businesses in a competitive
market.