1. Imperfect Competition
13-1

2. Drawing on Chapter 13
Copyright © The McGraw-Hill Companies, Inc. All rights reserved.

3. Overview Game theory and firms’ strategic interaction
Non-game-theoretic oligopoly models
Cournot
Bertrand
Stackelberg
Competition with increasing returns to scale
Monopolistic competition models
Chamberlin/Robinson
“Spatial”
Consumer preferences and advertising
13-3

4. Origins of Game Theory Sources of images, from left to right:
The book’s web page at Cambridge U. Press:
The Sept issue of Federation des Equipes Bull – Actualites:

5. Structure of Game Theory
Elements
Prediction/Solution
Players
Strategies
Payoffs
Timing
Information and communication
Dominant and dominated strategies
Nash equilibrium
Alternatives
Refinements of Nash equilibrium

6. Initial Solution Concepts
Dominant strategy
The strategy with better results for a player regardless of the other players’ strategy choices.
We predict that it will be played.
Dominated strategy
A strategy with worse results for a player regardless of the other players’ strategy choices.
We predict that one will never be played.
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7. Initial Solution Concepts (cont.)
Nash equilibrium
The combination of strategies with the best results for each player given the other players’ strategy choices.
From one, neither player has an incentive to change strategies unilaterally.
13-7

8. Example: Prisoner’s Dilemma
John
Oskar
Payoffs (years of prison sentence): Oskar John
Confess
Don’t Confess
Confess -5 -5
-10
Don’t confess
-10 -1 -1
13-8

9. Example: Capacity Expansion
Toyota VW
Payoffs ($M profit): VW Toyota
Build
Don’t Build
Build 16 16 20 15
Don’t Build 15 20 18 18
13-9

10. Example: Capacity Expansion
Toyota VW
Payoffs ($M profit): VW Toyota
Build
Don’t Build
Build 16 16 20 15
Don’t Build 15 20 18 18
13-10

11. Example: Capacity Expansion
Ambassador
Marutti
Payoffs ($M profit): Marutti Ambassador
Build
Don’t Build
Build 12 4 20 3
Don’t Build 15 6 18 5
13-11

12. Example: Capacity Expansion
Ambassador
Marutti
Payoffs ($M profit): Marutti Ambassador
Build
Don’t Build
Build 12 4 20 3
Don’t Build 15 6 18 5
13-12

13. Example: Capacity Expansion
Ambassador
Marutti
Payoffs ($M profit): Marutti Ambassador
Build
Don’t Build
Build 12 2 20 3
Don’t Build 15 6 18 5
13-13

14. Example: Capacity Expansion
Ambassador
Marutti
Payoffs ($M profit): Marutti Ambassador
Build
Don’t Build
Build 12 2 20 3
Don’t Build 15 6 18 5
13-14

15. Alternate Solution Concept
Maximin strategy:
Choosing the option that makes the lowest payoff one can receive (over the other players’ range of strategies) as large as possible.
13-15

16. Example: Research Spending
Intel
AMD
Payoffs ($M profit): AMD Intel
High
Low
High 10 20 14 18
Low 12 28 6 27
13-16

17. Example: Research Spending
Intel
AMD
Payoffs ($M profit): AMD Intel
High
Low
High 10 20 14 18
Low 12 28 6 27
13-17

18. Example: Capacity Expansion
Toyota VW
Payoffs ($M profit): VW Toyota
Build Large
Build Small
Don’t Build
Build Large 12 8 18 9
Build Small 8 12 16 16 20 15
Don’t Build 9 18 15 20 18 18
13-18

19. Example: Capacity Expansion
Toyota VW
Payoffs ($M profit): VW Toyota
Build
Don’t Build
Build 16 16 20 15
Don’t Build 15 20 18 18
13-19

20. Repeated Games: Strategies
Here a strategy is a plan for what to do in each interaction.
Examples for two-player games with two single-shot strategies:
Always cooperate.
Never cooperate.
Grim trigger: initially cooperate; if the other player does not, forever after do not.
Tit for tat: initially cooperate, then do what the other player did in the previous interaction.
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21. Repeated Games: Predictions
If the other plays grim trigger, what is better for you: always cooperate, or never cooperate? t
Coop
Not
Difference
PV(Difference)
PCC
PNC
PNC – PCC
(+) 1
PNN
PNN – PCC
(−)
(PNN – PCC)/(1+r) 2
(PNN – PCC)/(1+r)2
... T ...
... PCC...
...PNN...
(PNN – PCC)/(1+r)T
Total: 1∞
(PNN – PCC)/r
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22. Repeated Games: Conditions Fostering Cooperation
Not a known, fixed number of future interactions.
Patience: low discount rate and/or frequent interactions.
Small benefit of cheating on a cooperating counterpart.
Large cost of retaliation.
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23. Sequential Games Players alternate strategy choices
The second player responds to the first’s choice
The first player chooses accordingly
Examples with deterrence:
The US and USSR in the early Cold War
Entry deterrence: using a potential rival’s expectations of a firm’s response to a threat to its market position
13-23

24. Sequential Game Example
Small
Large
Don’t
VW 0, Toyota 0
Toyota
Large
VW 12, Toyota 8
VW 18, Toyota 9
Large
VW 8, Toyota 12
Toyota VW
Small
Small
VW 16, Toyota 16
Don’t
VW 20, Toyota 15
Small
Large
Don’t
VW 9, Toyota 18
Toyota
Don’t
VW 15, Toyota 20
VW 18, Toyota 18