1. Managerial Economics Game Theory
Aalto University
School of Science
Department of Industrial Engineering and Management
January 10 – 26, 2017
Dr. Arto Kovanen, Ph.D.
Visiting Lecturer

2. General considerations
We have considered three basic models of industrial structures:
Monopoly
Perfect competition and
Monopolistic competition (everything in between)
In the last case the action of the 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 will constitute a rather large part of the market; this is called oligopoly

3. General considerations
When there are only two firms, the structure is called duopoly
With few firms in the market, strategic interaction between the firms becomes 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

4. Game theory
So far we have assumed that each firm operates in a way that takes the actions of others given
Such behavior is sensible in a perfectly competitive market
When there are few players in a given market, the strategic interaction becomes very important for outcomes (for inputs as well as outputs)
That is, a decision of one participant has implications for the others’ decisions/outcomes
Game theory analyzes strategic interaction
Payoff matrix describes the strategic interaction and the related outcomes

5. Game theory What will be the outcome of the game?
How is the game played?
There are alternative set-ups for the games:
Are players cooperating or not?
Can each player only move once or take turns several times (repeated games)?
Is the game played infinitely or does it have finite steps?
In multi-stage games decisions are made at different stages of the game
It is also important to know if there is a dominant strategy (not always the case)
Are there rules/penalties for cheating in the game?

6. Game theory - example
Two-player game where the employee has to choose whether to spend $1,000 for work-related training while the employer has to decide whether to pay a fixed wage of $10,000 to the employee or share the revenue of the firm 50:50 with the employee
Firm’s output is positively affected by both training and revenue sharing
With no training and revenue-sharing, total output is worth $20,000
With either training or profit-sharing, total output is worth $22,000
With both training and profit-sharing, total output is worth $25,000

7. Game theory - example Construct a payoff matrix: EMPLOYER
EMPLOYEE Revenue-sharing Fixed wage
Training 11.5, ,12
No training 11.0, ,10
Is there a dominant strategy? For the employee, no, since he will only choose training if there is revenue-sharing. For the employer the dominant strategy is revenue-sharing
Is there a Nash equilibrium (i.e., neither has incentive to change strategy, given the other’s)? Yes, revenue-sharing and training, and fixed wage and no training

8. 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? Both prisoners know that 3 years in prison is better than 6 and zero is better than 1 year in prison
If both deny, they would of course be best off! But this is not a credible strategy
If one denies, the other one is better off by confessing
Lack of coordination important for the outcome!
Nash equilibrium is where both will confess (3, 3)

9. Game theory Challenge is how to coordinate the actions of players!
This applies to a wide range of economic and political situations, such as:
Arms control
If there is no way of making a binding agreement, both sides end up deploying missiles
Cheating in an oil cartel
If you think the other side will stick to the agreed quota, it will pay off to produce more than your own quota

10. 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

11. 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)

12. 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

13. 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)

14. 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?