Context and concepts
STRATEGY AND GAMES
w Context: You’re in an industry with a small number of competitors. You’re concerned that if you cut your price, your competitors will, too. How do you act? Ditto pretty much any strategic decision: capacity, entry and exit, product positioning. w Concepts: players, strategies, dominant and dominated strategies, best responses, Nash equilibrium. w Example: E.T. Whether Mars should buy a product placement for M&Ms.
© 2001 Cabral and Backus (10/26/01)
The field of strategy
Game theory w Formal analysis of strategic behaviour: relations between inter-dependent agents.
w Strategy includes: w Organizational structure and processes needed to implement the firm’s plan w Boundaries of the firm: scale, scope, extent of outsourcing w Formal analysis of strategic behaviour: game theory
w Informally, game theory reminds us to w Understand our competitors. Our results depend not only on our own decisions but on our competitors’ decisions as well. w Look into the future. Decisions taken today may have an impact in future decisions, both by ourselves and by our competitors. w Pay attention to information. Who knows what can make a difference. w Look for win-win opportunities. Some situations are competitive, but others offer benefits to all.
What they say
Overview
I think it is instructive to use game theory analysis... Game theory forces you to see a business situation over many periods from two perspectives: yours and your competitor’s. — Judy Lewent, CFO, Merck At their worst, game theorists represent a throw back to the days of such whiz kids as Robert McNamara … who thought that rigorous analytical skills were the key to success. Managers have much to learn from game theory -provided they use it to clarify their thinking, not as a substitute for business experience. — The Economist
w Our goal is to create an awareness of strategic considerations in many circumstances of business life (and, in fact, of everyday life). w Our focus is on how to play some common games: pricing, capacity, entry and exit, product positioning, and ways to encourage cooperation. w In practice, many of the benefits come from choosing the right games and avoiding the wrong ones. For example: avoid price games.
1
Historical notes
The E.T. “chocolate wars” In the movie “E.T.” a trail of Reese's Pieces, one of Hershey's chocolate brands, is used to lure the little alien into the house. As a result of the publicity created by this scene, sales of Reese's Pieces tripled, allowing Hershey to catch up with rival Mars.
[JvN, also co-inventor of the computer/ operating system.]
John von Neuman, precursor of game theory.
The 1995 U.S. spectrum auction was partly designed by game theorist Paul Milgrom .
John Nash, 1994 Nobel laureate, the first game theorist to receive the prize. Game theory is now commonly used by various consulting companies such as McKinsey.
Chocolate wars… w Universal Studio's original plan was to use a trail of Mars‘s M&Ms and charge Mars $1mm for the product placement. w However, Mars turned down the offer, presumably because it thought $1mm was high. w The producers of “E.T.” then turned to Hershey, who accepted the deal, which turned out to be very favorable to them (and unfavorable to Mars).
Mars 1: decision approach
buy
Chocolate wars… w Formal analysis of the E.T. game. w Suppose: w Publicity from the product placement increases Mars‘s profits by $800,000. w Hershey's increase in market share costs Mars $500,000. w Benefit to Hershey from having its brand featured is given by b. w Hershey knows the value of b. Mars knows only that b=$1,200,000 or b=$700,000 with equal probability.
Mars 2: naïve game theory
[-200]
M
buy
[-200, 0]
M not buy
not buy [0]
0
buy
[-500, -50]
H not buy
[0, 0]
2
Mars 3: real game theory
Quick summary w Think about your competitor: Mars should think about Hershey, and vice versa.
[-200, 0]
buy
buy
-500
M
b = 1200 (50%) not buy
-250
[-500, 200]
H not buy
[0, 0]
N b = 700 (50%)
buy
0
[-500, -300]
w Timing matters: Hershey had the last move. w Information matters: Hershey has more information than Mars, and in this example it made a difference. w Key business insight: part of the benefit to Mars was to keep the opportunity from Hershey. Similar situation: Boeing, Airbus, and the super-jumbo.
H not buy
[0, 0]
Game theory: concepts
Normal-form game
w What are the elements of a game? w w w w
Player B
Players (in previous example: Mars and Hershey) Rules (sequentially respond to Universal’s offer) Strategies (Yes or No) Payoffs (sales minus payment to Universal)
w What can I do with it? w Determine how good each of my strategies is w Figure out what my rival is probably going to do
T
L
C
5
6
9
8 3
Player A
M 1 2
7 1
5 2
7 B
R
6 0
6 3
8 4
Moves are simultaneous. Which make sense?
Dominant/dominated strategies w Dominant strategy: payoff is greater than any other strategy regardless of rival’s choice. w Rule 1: if there is one, choose it.
w Dominated strategy: payoff is lower than some other strategy regardless of rival’s choice. w Rule 2: do not choose dominated strategies.
w Are there dominant or dominated strategies in the example?
Outcomes of games w Sometimes a game can be “solved” just by looking at dominant and dominated strategies (e.g., example above). w However, there are many games for which this isn’t enough to produce an outcome. à Nash equilibrium: Combination of moves in which no player would want to change her strategy unilaterally. Each chooses its best strategy given what the others are doing.
3
Prisoner’s dilemma
w Dominant strategies: high output.
Iraq’s Output
Example: output setting (million barrels a day) by OPEC members
Iran’s Output
Prisoner’s dilemma…
2
2
4
42
44
46
26 22
4
52
24 32
Takeaways
w Equilibrium payoffs are (32,24), much worse than would be attained by low output, (46,42). w Conflict between individual incentives and joint incentives. w Typical of many business situations. w Are cartels inherently unstable?
Practice problem 2.7
w Game theory is a formal approach to strategy. L
w Highlights impact of strategic interactions among firms or other “players.”
2 T
w Forces you to consider your competitors’ choices. Player 1
w More coming…
Player 2 C
1
1 1
M 2
2
2
Practice problem 2.8 Time/Newsweek cover story game
Time
Imp
Imp Crisis 35,35 70,30
Crisis
30,70
15,15
1 2
4 0
3 3
Imp Time
• Dominated strategy? • Best responses?
• Dominant strategy? • Dominated strategy? • Best responses?
Practice problem 2.8…
Questions: • Dominant strategy?
Questions:
• Nash equilibrium?
Version (ii): Time more popular Newsweek
Version (i): evenly matched Newsweek
1 1
2
B 10
R
0
Crisis
Questions: • Dominant strategy?
Imp
42,28 70,30
• Dominated strategy?
Crisis
30,70
• Best responses?
18,12
• Nash equilibrium? Version (iii): Some buy both
• Nash equilibrium? Time
Imp
Crisis
Imp
42,28
70,50
Crisis
50,70
30,20
Comment: This is a product positioning game. The question is whether to fight head-to-head or differentiate. Answer: It depends!
4
Ericsson v Nokia
Ericsson v Nokia…
w Ericsson and Nokia compete on 4G handsets. Two possible price levels: $100 and $90. Production cost is $40. Estimated market demand (000 per quarter):
w Suppose firms choose prices simultaneously. Describe the game and solve it.
Nokia’s price 100 90 800 100
900
90
900
Ericsson’s price
700
Estimated profit ($m per quarter):
Nokia’s price 100 90
1,100
48
400
Ericsonn’s price
900 *
800
Ericsson v Nokia… w Both Ericsson and Nokia have a dominant strategy: price at $90. The Nash equilibrium of this game is therefore (90,90), leading to profits of (40,45) for Ericsson and Nokia, respectively.
30m = (100-40) 500k
100
30*
90
45
42
w Suppose that Nokia has a limited capacity of 900k units per quarter. How would the analysis change? (Changes in yellow.) Estimated profit ($mm per quarter):
Nokia’s price 100 90 48 100
24 42
w Your CIO is unsure whether Nokia is capacity constrained or not. How much would you value this piece of info? How would your strategy depend on it?
36
45
90
w Suppose you work for Ericsson. Your market research team tells you that practically 100% of all unfulfilled demand for Nokia will be transferred to Ericsson.
45
30
Ericsson’s price
w It is now a dominant strategy for Nokia to price at $100. It is still a dominant strategy for Ericsson to price at $90.
45 40
Ericsson v Nokia 2
w Notice that both Ericsson and Nokia are worse off than they would be by pricing at $100. This game has the structure of a prisoner’s dilemma.
Ericsson v Nokia 2…
55 24
40
Coke v Pepsi w
You work for Pepsi. The company has just signed a major star endorsement. You must decide how much to spend on for your Summer ad campaign. Net profits (in $m) depend on how much you and Coke spend – and on whether or not Coke has signed a major star: Coke’s adv 2 1 3 Pepsi’s adv
2
0
1
1
Coke’s adv 2 1
2 1
4
5 2
(a) Coke signed major star
0 Pepsi’s adv
2
4
1
2
1 6
2
3 3
(b) Coke did not
5
Coke v Pepsi…
Coke v Pepsi intuition
w Coke’s decision of whether to sign a major star has already been taken. You don’t know what the decision was. Your CIO tells you that there is a 70% chance they did. w You also know that Coke will have a chance to react to your decision of how much to spend. w Should you go for a $1m or a $2m campaign?
w
This is a sequential game with incomplete information. Let us solve it backwards and include “Nature” as a player.
w
If Coke did sign a star, then it will choose $2m if and only if Pepsi chooses $2m. If Coke did not sign a star, then it will choose $1m regardless of what Pepsi chooses.
w
Moving backwards: w If Pepsi chooses $1m, then Coke will choose $1m. Pepsi’s expected payoff is 70% 2 + 30% 3 = $2.3m. w If Pepsi chooses $2m, then Coke will choose $2m with probability 70%, $1m with probability 30%. Pepsi’s expected payoff is 70% 0 + 30% 6 = $1.8m. w Pepsi should choose $1m. (What considerations are we leaving out of the analysis?)
Coke v Pepsi game tree P 70% 2 + + 30% 3 = 2.3
1
2
N
N
star (70%)
no star (80%)
C
70% 0 + + 30% 6 = 1.8
star
C
no star (80%)
C
C
1
2
1
2
1
2
1
2
2
1
3
2
1
0
6
4
5
4
3
2
2
3
1
0
6
