1. Managerial Economics & Business Strategy
Chapter 10
Game Theory: Inside Oligopoly

2. Introduction: Prisoner’s Dilemma
Ginger and Rocky rob a 7-eleven. Evidence is good on the robbery but not so good on whether it was an armed robbery.
Rocky
Strategy
Don’t Confess
Confess
1, 1
7, Free
Free, 7
5, 5
Ginger

3. Introduction: Prisoner’s Dilemma
Game Theory on Display (tires example)
EC Fines Roche, BASF, Six Other Firms Total of $751.7 million for Price Fixing, WSJ 2001

4. Game Form A Normal Form Game consists of:
Players = managers or firms
Strategies or feasible actions = planned decisions
Payoffs = profits or losses, market share
The order in which players make decisions is important
Simultaneous
Sequential
Type of game is important
one-shot
repeated games

5. 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

6. Normal Form Game: Scenario Analysis
Suppose 1 thinks 2 will choose “A”.
Player 2
12,11
11,12
14,13
Player 1
11,10
10,11
12,12
10,15
10,13
13,14

7. Normal Form Game: Scenario Analysis
Then 1 should choose “a”.
Player 1’s best response to “A” is “a”.
Player 2
12,11
11,12
14,13
Player 1
11,10
10,11
12,12
10,15
10,13
13,14

8. Normal Form Game: Scenario Analysis
Suppose 1 thinks 2 will choose “B”.
Player 2
12,11
11,12
14,13
Player 1
11,10
10,11
12,12
10,15
10,13
13,14

9. Normal Form Game: Scenario Analysis
Then 1 should choose “a”.
Player 1’s best response to “B” is “a”.
Player 2
12,11
11,12
14,13
Player 1
11,10
10,11
12,12
10,15
10,13
13,14

10. Normal Form Game Scenario Analysis
Similarly, if 1 thinks 2 will choose C…
Player 1’s best response to “C” is “a”.
Player 2
12,11
11,12
14,13
Player 1
11,10
10,11
12,12
10,15
10,13
13,14

11. Dominant Strategy
Regardless of whether Player 2 chooses A, B, or C, Player 1 is better off choosing “a”!
“a” is Player 1’s Dominant Strategy!
Player 2
12,11
11,12
14,13
Player 1
11,10
10,11
12,12
10,15
10,13
13,14

12. 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
Strategy A B C a b c
12,11
11,12
14,13 C
Player 1
11,10
10,11
12,12
10,15
10,13
13,14 C A

13. The Outcome This outcome is called a Nash equilibrium: Player 2 12,11
11,12
14,13
Player 1
11,10
10,11
12,12
10,15
10,13
13,14
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”.

14. Key Insights Look for dominant strategies
Put yourself in your rival’s shoes
Nash Equilibrium: doing the best you can given what other players are doing. No player can unilaterally improve his/her payoff by changing his/her strategy.
Not all games will have a Nash Equilibrium (monitoring workers example)
Some games may have more than 1 Nash Equilibrium

15. A Market Share Game
Two managers want to maximize market share (the payoff is market share)
Strategies are pricing decisions
Simultaneous moves
One-shot game

16. The Market-Share Game in Normal Form
Manager 2
Manager 1
First number in each cell represents the market share for Firm 1, and the second for Firm 2.

17. Market-Share Game Equilibrium
Manager 2
Manager 1
Nash Equilibrium

18. A Coordination Game Strategy Work Together Don’t Work Together
Microsoft Word
Strategy
Work Together
Don’t Work Together
$100, $80
$40, $40
$25, $25
$50, $80
Corel WordPerfect

19. A Coordination Problem: Two Nash Equilibria!
Microsoft Word
Strategy
Work Together
Don’t Work Together
$100, $80
$40, $40
$25, $25
$50, $80
Corel WordPerfect

20. Key Insights:
Not all games are games of conflict (e.g., industry standards existed for floppy disc sizes, electrical currents, new “industries,” HDTV)
Communication can help solve coordination problems.
Sequential moves can help solve coordination problems.
Government could set a standard to solve coordination problems: electrical current.

21. An Advertising Game
Two firms (Kellogg’s & General Mills) managers want to maximize profits
Strategies consist of advertising campaigns
Simultaneous moves
One-shot interaction
Repeated interaction

22. A One-Shot Advertising Game
General Mills
Kellogg’s

23. Equilibrium to the One-Shot Advertising Game
General Mills
Kellogg’s
Nash Equilibrium

24. Can collusion work if the game is repeated 1 time?
General Mills
Kellogg’s

25. No (by backwards induction).
In period 2, the game is a one-shot game, so equilibrium entails High Advertising in the last period.
The same holds true if we repeat the game any known, finite number of times.

26. Can collusion work if firms play the game each year, forever?
Yes, unless a rival “cheats.” Collusion can be supported with trigger strategies.
Consider the following “trigger strategy” by each firm:
“Don’t advertise, provided the rival has not advertised in the past. If the rival ever advertises, “punish” it by engaging in a high level of advertising forever after.”
In effect, each firm agrees to “cooperate” so long as the rival hasn’t “cheated” in the past. “Cheating” triggers punishment in all future periods.
Note: collusion illegal and it is illegal for firms to engage in “trigger-like” behavior to get the collusive outcome.

27. Suppose General Mills adopts this trigger strategy. Kellogg’s profits?
Cooperate = /(1+i) + 12/(1+i)2 + 12/(1+i)3 + …
= /i
Value of a perpetuity of $12 paid
at the end of every year
Cheat = 20 +2/(1+i) + 2/(1+i)2 + 2/(1+i)3 +
= /i
General Mills
Kellogg’s

28. Kellogg’s Gain to Cheating:
Cheat - Cooperate = /i - ( /i) = /i
Suppose i = .05
Cheat - Cooperate = /.05 = = -192
It doesn’t pay to deviate.
Collusion is a Nash equilibrium in the infinitely repeated game!
UGH!
General Mills
Kellogg’s

29. Key Insight
Collusion can be sustained as a Nash equilibrium when there is no certain “end” to a game.
Doing so requires:
Know your rival, your rival’s customers, and be able to monitor
Ability (and reputation for) punishing cheaters
Low interest rate (in this example, i ≤ 5/4)
High probability of future interaction
In infinitely repeated games there is always a tomorrow to consider. Must weigh the benefits and costs of cheating.

30. Real World Example of Collusion: OPEC
Cartel founded in 1960 by Iran, Iraq, Kuwait, Saudi Arabia, and Venezuela.
OPEC's mission is to coordinate and unify the petroleum policies of Member Countries and ensure the stabilization of oil markets in order to secure an efficient, economic and regular supply of petroleum to consumers, a steady income to producers and a fair return on capital to those investing in the petroleum industry. (

31. Cournot Game in Normal Form
Venezuela
Saudi Arabia
High Q is never a good strategy for either country; this essentially, means the game is between Med and Low.

32. One-Shot Cournot (Nash) Equilibrium
Venezuela
Saudi Arabia

33. Repeated Game Equilibrium*
Venezuela
Saudi Arabia
(Assuming a sufficiently low interest rate)

34. Caveat
Collusion is a felony under Section 2 of the Sherman Antitrust Act.
Conviction can result in both fines and jail-time (at the discretion of the court).
OPEC isn’t illegal; thus, US laws don’t apply

35. Simultaneous-Move Bargaining Game (SMBG)
Management and a union are negotiating a wage increase.
Strategies are wage offers & wage demands
Successful negotiations lead to $600 million in surplus, which must be split among the parties
Failure to reach an agreement results in a loss to the firm of $100 million and a union loss of $3 million
Simultaneous moves, and time permits only one-shot at making a deal.

36. The SMBG in Normal Form
Union
Management

37. Three Nash Equilibria!
Union
Management

38. Fairness
SMBG are difficult to predict because of multiple Nash Equilibria. Experimental evidence suggests that bargainers often perceive a split to be fair.
Union
Management

39. Single Offer Bargaining
Now suppose the game is sequential in nature, and management gets to make the union a “take-it-or-leave-it” offer.
Do the following: write the game in extensive form
Summarize the players
Their potential actions
Their information at each decision point
The sequence of moves and
Each player’s payoff

40. Step 1: Management’s Move10 5
Firm 1

41. Step 2: Add the Union’s Move
Accept
Union
Reject 10
Accept 5
Firm
Union
Reject 1
Accept
Union
Reject

42. Step 3: Add the Payoffs Accept 100, 500 Union -100, -3 Reject 10
300, 300 5
Firm
Union
-100, -3
Reject 1
Accept
500, 100
Union
-100, -3
Reject

43. Step 6: Identify Nash Equilibrium Outcomes
Outcomes such that neither the firm nor the union has an incentive to change its strategy, given the strategy of the other

44. There are 3 Nash Equilibrium Outcomes!
Accept
100, 500
Union
-100, -3
Reject 10
Accept
300, 300 5
Firm
Union
-100, -3
Reject 1
Accept
500, 100
Union
-100, -3
Reject

45. Only 1 Subgame-Perfect Nash Equilibrium Outcome!
Accept
100, 500
Union
-100, -3
Reject 10
Accept
300, 300 5
Firm
Union
-100, -3
Reject 1
Accept
500, 100
Union
-100, -3
Reject

46. Re-Cap
In take-it-or-leave-it bargaining, there is a first-mover advantage (what if union made offer, and firm had to take or leave it?). But...
Management should be careful, however; real world evidence suggests that people sometimes reject offers on the the basis of “principle” instead of cash considerations.
While the outcome was obvious, the framework can be used to analyze more complicated bargaining issues.

47. Pricing to Prevent Entry: An Application of Game Theory
Two firms: an incumbent and potential entrant
Incumbent threatens to start a price war. Is this credible?
The game in extensive form:

48. The Entry Game in Extensive Form
-1, 1
Price War
Incumbent
Enter
No Price War
5, 5
Entrant
Out
0, 10

49. One Subgame Perfect Equilibrium
Entrant
Out
Enter
Incumbent
Price War
No Price War
-1, 1
5, 5
0, 10

50. Incumbant VS. Entrant: Incumbant and Credible Threat
($2m), ($2m)
Enter
Entrant
Don’t Enter
Expand Q
$4m, $0
Incumbent
$2m, $2m
Enter
Don’t Expand Q
Entrant
Don’t Enter
$6m, $0

51. Incumbant VS. Entrant: Incumbant and Credible Threat
Nash and Subgame Perfect Nash: Expand and Don’t Enter
($2m), ($2m)
Enter
Entrant
Don’t Enter
Expand Q
$4m, $0
Incumbent
$2m, $2m
Enter
Don’t Expand Q
Entrant
Don’t Enter
Note: would see different outcome if entrant goes first (and has started its entry), then incumbant threat not credible.
$6m, $0

52. Insight
It does not pay to heed threats made by rivals because not all threats are credible.