1. Chapter 10 Game Theory and Strategic Behavior
Managerial Economics in a Global Economy, 5th Edition by Dominick Salvatore
Chapter 10
Game Theory and Strategic Behavior

2. Strategic Behavior
Decisions that take into account the predicted reactions of rival firms
Interdependence of outcomes
Game Theory
Players
Strategies
Payoff matrix

3. Strategic Behavior Types of Games Zero-sum games Nonzero-sum games
Nash Equilibrium
Each player chooses a strategy that is optimal given the strategy of the other player
A strategy is dominant if it is optimal regardless of what the other player does

4. Advertising Example 1

5. Advertising Example 1
What is the optimal strategy for Firm A if Firm B chooses to advertise?

6. Advertising Example 1
What is the optimal strategy for Firm A if Firm B chooses to advertise?
If Firm A chooses to advertise, the payoff is 4. Otherwise, the payoff is 2. The optimal strategy is to advertise.

7. Advertising Example 1
What is the optimal strategy for Firm A if Firm B chooses not to advertise?

8. Advertising Example 1
What is the optimal strategy for Firm A if Firm B chooses not to advertise?
If Firm A chooses to advertise, the payoff is 5. Otherwise, the payoff is 3. Again, the optimal strategy is to advertise.

9. Advertising Example 1
Regardless of what Firm B decides to do, the optimal strategy for Firm A is to advertise. The dominant strategy for Firm A is to advertise.

10. Advertising Example 1
What is the optimal strategy for Firm B if Firm A chooses to advertise?

11. Advertising Example 1
What is the optimal strategy for Firm B if Firm A chooses to advertise?
If Firm B chooses to advertise, the payoff is 3. Otherwise, the payoff is 1. The optimal strategy is to advertise.

12. Advertising Example 1
What is the optimal strategy for Firm B if Firm A chooses not to advertise?

13. Advertising Example 1
What is the optimal strategy for Firm B if Firm A chooses not to advertise?
If Firm B chooses to advertise, the payoff is 5. Otherwise, the payoff is 2. Again, the optimal strategy is to advertise.

14. Advertising Example 1
Regardless of what Firm A decides to do, the optimal strategy for Firm B is to advertise. The dominant strategy for Firm B is to advertise.

15. Advertising Example 1
The dominant strategy for Firm A is to advertise and the dominant strategy for Firm B is to advertise. The Nash equilibrium is for both firms to advertise.

16. Advertising Example 2

17. Advertising Example 2
What is the optimal strategy for Firm A if Firm B chooses to advertise?

18. Advertising Example 2
What is the optimal strategy for Firm A if Firm B chooses to advertise?
If Firm A chooses to advertise, the payoff is 4. Otherwise, the payoff is 2. The optimal strategy is to advertise.

19. Advertising Example 2
What is the optimal strategy for Firm A if Firm B chooses not to advertise?

20. Advertising Example 2
What is the optimal strategy for Firm A if Firm B chooses not to advertise?
If Firm A chooses to advertise, the payoff is 5. Otherwise, the payoff is 6. In this case, the optimal strategy is not to advertise.

21. Advertising Example 2
The optimal strategy for Firm A depends on which strategy is chosen by Firms B. Firm A does not have a dominant strategy.

22. Advertising Example 2
What is the optimal strategy for Firm B if Firm A chooses to advertise?

23. Advertising Example 2
What is the optimal strategy for Firm B if Firm A chooses to advertise?
If Firm B chooses to advertise, the payoff is 3. Otherwise, the payoff is 1. The optimal strategy is to advertise.

24. Advertising Example 2
What is the optimal strategy for Firm B if Firm A chooses not to advertise?

25. Advertising Example 2
What is the optimal strategy for Firm B if Firm A chooses not to advertise?
If Firm B chooses to advertise, the payoff is 5. Otherwise, the payoff is 2. Again, the optimal strategy is to advertise.

26. Advertising Example 2
Regardless of what Firm A decides to do, the optimal strategy for Firm B is to advertise. The dominant strategy for Firm B is to advertise.

27. Advertising Example 2
The dominant strategy for Firm B is to advertise. If Firm B chooses to advertise, then the optimal strategy for Firm A is to advertise. The Nash equilibrium is for both firms to advertise.

28. A Normal Form Game Player 2 12,11 11,12 14,13 Player 1 11,10 10,11
12,12
10,15
10,13
13,14

29. Putting Yourself in your Rival’s Shoes
What should player 2 do?
2 has no dominant strategy!
But 2 should reason that 1 will play “a”.
Therefore 2 should choose “C”.
Player 2
12,11
11,12
14,13
Player 1
11,10
10,11
12,12
10,15
10,13
13,14

30. The Outcome This outcome is called a Nash equilibrium:
Player 2
12,11
11,12
14,13
11,10
10,11
12,12
10,15
10,13
13,14
Player 1
This outcome is called a Nash equilibrium:
“a” is player 1’s best response to “C”.
“C” is player 2’s best response to “a”.

31. The Market-Share Game in Normal Form
Manager 2
Manager 1

32. No Equilibrium - Child’s play
Player 2
Player 1

33. Multiple Equilibria - Battle of the Sexes
Him
Her

34. Prisoners’ Dilemma
Two suspects are arrested for armed robbery. They are immediately separated. If convicted, they will get a term of 10 years in prison. However, the evidence is not sufficient to convict them of more than the crime of possessing stolen goods, which carries a sentence of only 1 year.
The suspects are told the following: If you confess and your accomplice does not, you will go free. If you do not confess and your accomplice does, you will get 10 years in prison. If you both confess, you will both get 5 years in prison.

35. Payoff Matrix (negative values)
Prisoners’ Dilemma
Payoff Matrix (negative values)

36. Dominant Strategy Both Individuals Confess
Prisoners’ Dilemma
Dominant Strategy Both Individuals Confess
(Nash Equilibrium)

37. Normal Form Game (Simultaneous Movers - Prisoner’s Dilemma)
Environment - Police station after a crime wave. Police have evidence on a minor crime. Police have insufficient evidence on major crime
Players - Bonnie and Clyde
Rules - no escape is possible
Strategies - Rat or not rat
Payoffs -
No one rats: both get 3 years
One rats and the other stays quiet: rat gets 1 year, Silent partner gets 23 years
Both rat: both get 16 years

38. The Normal Form of Prisoner’s Dilemma
Bonnie
16,16
1, 23
Clyde
23,1
3,3

39. Resolving Bonnie & Clyde
If Bonnie Rats and
Clyde doesn’t rat, then Bonnie gets 1 year
Clyde rats, then Bonnie gets 16 years
If Bonnie doesn’t Rat and
Clyde doesn’t rat, then Bonnie gets 3 years
Clyde rats, then Bonnie gets 23 years
If Clyde Rats and
Bonnie doesn’t rat, then Clyde gets 1 year
Bonnie rats, then Clyde gets 16 years
If Clyde doesn’t Rat and
Bonnie doesn’t rat, then Clyde gets 3 years
Bonnie rats, then Clyde gets 23 years

40. Resolving Bonnie & Clyde
Bonnie has a dominant strategy - Rat
Clyde has a dominant strategy - Rat
Nash Equilibrium - set of strategies that are “best responses” to each other
Nash here is: {Rat; Rat}
Payoffs here are: {16 years; 16 years}
Best outcome is {Don’t Rat; Don’t Rat} with payoffs of {3 yrs; 3 years}
How do we get cooperation?
Suppose each promised the other not to rat?

41. Application: Price Competition
Prisoners’ Dilemma
Application: Price Competition

42. Application: Price Competition Dominant Strategy: Low Price
Prisoners’ Dilemma
Application: Price Competition Dominant Strategy: Low Price

43. Application: Nonprice Competition
Prisoners’ Dilemma
Application: Nonprice Competition

44. Application: Nonprice Competition Dominant Strategy: Advertise
Prisoners’ Dilemma
Application: Nonprice Competition Dominant Strategy: Advertise

45. Application: Cartel Cheating
Prisoners’ Dilemma
Application: Cartel Cheating

46. Application: Cartel Cheating Dominant Strategy: Cheat
Prisoners’ Dilemma
Application: Cartel Cheating Dominant Strategy: Cheat

47. Extensions of Game Theory
Repeated Games
Many consecutive moves and countermoves by each player
Tit-For-Tat Strategy
Do to your opponent what your opponent has just done to you

48. Extensions of Game Theory
Tit-For-Tat Strategy
Stable set of players
Small number of players
Easy detection of cheating
Stable demand and cost conditions
Game repeated a large and uncertain number of times

49. Extensions of Game Theory
Threat Strategies
Credibility
Reputation
Commitment
Example: Entry deterrence

50. Entry Deterrence No Credible Entry Deterrence

51. Entry Deterrence No Credible Entry Deterrence

52. International Competition
Boeing Versus Airbus Industrie

53. Sequential Games Sequence of moves by rivals
Payoffs depend on entire sequence
Decision trees
Decision nodes
Branches (alternatives)
Solution by reverse induction
From final decision to first decision

54. High-price, Low-price Strategy Game

55. High-price, Low-price Strategy GameX X

56. High-price, Low-price Strategy GameX
Solution:
Both firms choose low price. X X

57. Airbus and Boeing

58. Airbus and Boeing X X

59. X X X Airbus and Boeing Solution:
Airbus builds A380 and Boeing builds Sonic Cruiser. X X

60. Integrating Case Study