Managerial Economics
Game Theory
Aalto University
School of Science
Department of Industrial Engineering and Management
January 12 – 28, 2016
Dr. Arto Kovanen, Ph.D.
Visiting Lecturer
General considerations
 We have considered three models of industrial
structures, monopoly, pure competition, and
monopolistic competition (everything in between)
 In the last two cases the action of each firm depends
on the actions of other firms
 We can assume that the actions of other are given to
a firm if each firm is relatively small
 When there are few firms, each firm constitute a
rather large part of the market; this is called oligopoly
General considerations
 When there are only two firms, the structure is called
duopoly
 With few firms in the market, strategic interaction
between the firms become an important part of the
outcome
 In what follows, we discuss alternative strategic
interactions between firms and how they impact
production and pricing decisions
 To limit the power of oligopolies, there are public
policy issues which we discuss later
Game theory
 Game theory analyzes strategic interaction
 Payoff matrix describes the strategic interaction
 Assume two individuals
 Person A will write one of two words on a piece of paper,
“top” or “bottom”
 Simultaneously, person B will independently write words
“left” or “right” on a piece of paper
 Suppose that the payoff matrix of the game will be
Person B
Left
Right
Person A
Top
1,2
0,1
Bottom 2,1
1,0
Game theory








What will be the outcome of the game?
For person A it is always better to say “bottom”
For person B it is always better to say “left”
In this game, there is a dominant strategy:
bottom/left
This will be also the equilibrium strategy
However, dominant strategies do not always happen
Suppose there is no dominant strategy for the game
Then the optimal choice depends on what the player
thinks the other person is going to do
Game theory
Person A
Top
Bottom
Person B
Left
Right
2,1
0,0
0,0
1,2
 Nash equilibrium: a pair of strategies where A’s choice
is optimal given B’s choice and B’s choice is optimal
given A’s choice
 Neither person know what the other is going to do,
but can have expectations about it
 In the above table, the combination of “top”/”left” is
a Nash equilibrium (this is optimal for both)
Game theory
 The Nash has some problems:
 First, there may be more than one equilibrium (choice
“bottom”/”right” is a feasible)
 Some games have no Nash equilibrium
 See also:
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Mixed strategies: pure and mixed
Prisoner’s dilemma
Repeated games
Sequential games
Game theory
 Prisoner’s dilemma – payoff matrix (years in prison)
Prisoner B
Confess
Deny
Prisoner A
Confess
-3, -3
0, -6
Deny
-6, 0
-1, -1
 What is the best outcome?
 If both deny, they would of course be best off! Is it
credible?
 If one denies, the other one is better off by confessing
 Lack of coordination important for the outcome!
Game theory
 Problem is how to coordinate the actions!
 This applies to a wide range of economic and political
situations
 Arms control: if there is no way of making a binding
agreement, both sides end up deploying missiles
 Cheating in a cartel: if you think the other side will stick to
the agreed quota, it will pay off to produce more than
your own quota
Game theory
 Sequential games
 There are situations where one player gets to move
first and then the second player responds
(Stackelberg)
A chooses
A choose

B chooses Left (1,9)

B chooses Right (1,9)

B chooses Left (0,0)

B chooses Right (2,1)
Top
Bottom
Game theory
 To analyze this game, work backwards
 If player A chooses “Top”, B’s choice does not matter
for his payoff (1, 9)
 If player A chooses “Bottom”, it matters what B
chooses
 But player A is better of choosing “Bottom”
 Practical example: monopoly fights to avoid entrance
of a new firm in the market (“pre-emptive” action)
 Could also apply to a oligopoly where a dominant firm
encourages entry by lowering the threshold price
below cost for others (for instance, Saudi oil and US
shale gas)
Game theory – Cournot model
 This model is relevant for markets where two firms are
competing, but also applies to markets with few firms
(e.g., Coca-Cola and Pepsi)
 Firms produce homogeneous products
 There are many buyers
 Each firm determines its output based on the other’s
action (estimated)
 Example. Let market demand be P = 400 – 2*(Q1+Q2)
 Each firm has MC = $ 40 and no fixed costs
Game theory – Cournot model
 Profits of each firm are as follows:
π1 = (400 – 2Q1 – 2Q2)Q1 – 40Q1
= 360Q1 – 2Q22 – 2Q1*Q2
(The second firm has a similar profit function)
 Solve for optimal output for firm 1:
dπ1 = dQ1 = 0, which gives us Q1 = 90 – 0.5Q2
 Note that firm 1 does not know the value of Q2 with
certainty and therefore has to estimate it (e.g., based
on total market demand forecast in which Q2 would be
a residual)
Game theory – Cournot (cont.)
 The equilibrium is found in the intersection of the
firms’ optimal positions (which depend on the other
firm’s reaction function)
 That is, solve for
Q1 = 90 – 0.5Q2
Q2 = 90 – 0.5 Q1
 Since firms are identical, the optimal Q1 = Q2 = 60 for
both firms
 Given total production of 120, P = 400 – 2*120 = $ 160
 Illustrate the strategic interaction between these firms
in the market
Game theory – Cournot (cont.)
 The game changes a bit if one of the firms is a “leader”
while the other is a “follower”
 For the follower the optimal outcome is the same as
above (i.e., follower is taking into account the leader’s
possible action)
 The leader, on the other hand, does not account for
the follower’s action when determining its output
 P(L) = 400 – 2*[Q(L) + (90 – 0.5*Q(L))]

= 220 – Q(L)
π(L) = (220 – Q(L))*Q(L) – 40*Q(L), which gives us Q(L)
equal to 90 (which is higher than 60 above)
Game theory – Cournot (cont.)
 The follower will then produce Q(F) = 45 and P = $ 130
 Comparison to Cournot equilibrium, we observe that
 P is lower
 Q(L) is higher and Q(F) is lower
 Profits of the leader are higher and profits of the follower
are lower
 Total industry profits lower because total output is higher
and hence price has to come down in equilibrium
 Examples of market leaders: Is Apple a market leader in
smart phone markets (not homogeneous products and
what is means for pricing)?
 Homogeneous products: Banks and cuts in loan rates?