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MBA 299 – Section Notes

5/9/03

Haas School of Business, UC Berkeley

Rawley

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AGENDA

Old exam questions (5-7)

Dominant strategies

Nash equilibrium (NE)

IDSDS

Repeated games and SPNE

Cournot equilibrium

Suggested answers to the conceptual (old) exam questions

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OLD FINAL EXAM QUESTIONS: #5

Q: Which of the following statements about the inferior technology used by the fringe firms is correct?

Answer A:

LRAC = $10

Eliminate option D. since if AC and MC are >$10 the fringe would never be willing to sell at $10

If MC falling at $10 then LRAC is declining, similarly if MC is rising at $10 then LRAC is falling so B. and C. do not make sense as options here

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OLD FINAL EXAM QUESTIONS: #6

Q: A number of possible marginal revenue curves for the one firm with the superior technology are also illustrated

Answer D:

MR = dR/dQ

Market demand is not the same as firm specific demand

If this was a monopoly (supply) market then ACEF is the MR curve, but since there are at least two firms producing here (note the other MR curve at HG), the market price is $10, after point H the situation is just like the monopoly situation again . . . therefore MR is flat from B to H and then follows the “normal” MR curve from E to F

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OLD FINAL EXAM QUESTIONS: #7

Q: Find the equilibrium set of prices (in a sealed bid auction)

Answer D: 3 NE in this game

Do NOT use IDWDS (as I did in class last week)

0,0 0,0 0,0

0,0 ½, ½ 1,0

0,0 0,1 1,1

400

401

402

400 401 402

1

2

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DOMINANT STRATEGIESBest Strategy Regardless of What the Other Player Does

1,0 0,0 0, ½

0,0 ½, ½ 1,1

0,0 0,1 0,2

U

M

D

L B R

1

2

0,0 0,0 0, ½

1,0 ½, ½ 1,1

0,0 0,1 0,2

U

M

D

L B R

1

2

2 has a DS {R}, but 1 does notso there is no solution in DS

notice that MR is a NE

2’s DS is R, 1’s DS is M so the solution in DS is (M,R)

notice that MR is a NE too

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NASH EQUILIBRIUMBest Response Given the Other Player’s Strategy

1,1 0,0 0, ½

0,0 ½, ½ 1,0

0,0 0,1 0,2

U

M

D

L B R

1

2

1,1 0,0 0, ½

0,99 ½, ½ 100,98

0,0 0,1 99,99

U

M

D

L B R

1

2

2 Nash Equilibria (U,L) and {B,M}

NE is {U,L}

Notice this outcome is not efficient

Every game has a NEEvery game has a NE

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ITERATED DELETION OF STRICTLY DOMINATED STRATEGIES (IDSDS): Problem #4 P.S. #1

Eliminate Strategies That Will Never Be Played in EQM

8,5 2,4

5,4 6,3

4,1 4,8

L R

U

M

D

1

2

First eliminate row D, next eliminate column R

Solution in IDSDS is also a NE

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REPEATED GAMES & SPNECredible Threats Can Shift the EQM in a Repeated Game

1,1 5,0 0,0

0,5 4,4 0,0

0,0 0,0 3,3

U

M

D

L C R

1

2

If each player believes the otherplayer will punish them with the lower NE in stage 2 if they fail toplay C or M in stage 1 (respectively)

then the unique SPNE in this stage game played twice without discounting is (M,C), (D,R)

Note: Stage game NE underlined here

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PROBLEM SET #2 QUESTION 1: COURNOT EQM (I)

Q(p) = 2,000,000 - 50,000pMC1 = MC2 = 10

a.) Find the Cournot EQM

P(Q) = 40 - Q/50,000

Find each firm’s mutual best responsei = qi[P(Q)-c] = qi[40 – Q/50,000 -10] = qi[40 – [qi+qj]/50,000 -10] = j

For both firm’s their best play is to maximize profit, therefore take the derivative of the profit function and set it equal to zero

d i/dqi = 40qi –[qi2 + qiqj]/50,000 – 10qi

= 40 – [2qi + qj]/50,000 – 10 = 0=> 2qi + qj = 1,500,000 => 3qi = 1,500,000q1=q2=500,000

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PROBLEM SET #2 QUESTION 1: COURNOT EQM (II)

b.) What is the profit for each firm in EQM?

i = (p-c)*qi = (40-1,000,000/50,000-10)*500,000 = $5M

c.) What is the monopoly profit level?

Setting MR = MC

MR = dP(Q)/dQ*Q + P(Q) = -Q/50,000 + 40 - Q/50,000 = 40 –Q/25,000

MC = 10

40 –Q/25,000 = 10 Q = 750,000 P = $25

=> m = (25-10)*750,000=$11.25M

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SUGGESTED ANSWERS TO SHORT ANSWER QUESTIONS: Question #11 (I)

Warning: These are Evan’s Answers Not Professor Hermalin’s

Part a.) Two possible reasons why Tartot cards are $5 and palm reading $1

Physical barrier to entry: The capital outlay required for Tarot cards represent a barrier to entry (BTE). Street vendors tend to face borrowing constraints so capital outlays can be important BTE. As with any BTE, restrictions on entry allow the owners of the assets to “permanently” increase price above long-run average cost.

Human capital barrier to entry: While anyone can sound credible reading a palm sounding credible when reading Tarot cards might take some specialized investment in human capital. In this context we view tarot card readers as “prepared” types and palm readers and “unprepared” types where prepared types earn rents for erecting human capital barriers to entry.

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SUGGESTED ANSWERS TO SHORT ANSWER QUESTIONS: Question #11 (II)

Warning: These are Evan’s Answers Not Professor Hermalin’s

Part b.) Sensible strategies for Farrell and Saloner

Because intellectual property (IP) cannot be used as the basis of sustainable competitive advantage F & S will drive profit to zero through a form of Bertrand competition if they do not coordinate on either price or R&D spend dimensions. Explicitly coordinating on price is illegal, tacit collusion, however, may be possible since this is duopoly competition in a repeated game. If F & S could send each other credible signals that deviation from a cooperative outcome (say cost +x%) would be punished in future rounds (with say marginal cost pricing) it may be possible to sustain equilibrium prices above marginal cost.

Coordinating on R&D is another solution. F & S could form a joint venture to manage all R&D activity where the R&D entity was paid cost plus a x% markup. F & S could then take the (same) raw technology and compete against one another for contracts on the basis of implementation efficiency.

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SUGGESTED ANSWERS TO SHORT ANSWER QUESTIONS: Question #11 (III)

Warning: These are Evan’s Answers Not Professor Hermalin’s

Part c.) Katz-Shapiro network cards

Since the nature of KS’s product is networking KS’s installed base acts a network externality, or a demand side economy of scale, which supports its dominant market position. However, KS earns most of it’s profits from services supporting it’s network software, therefore it is potentially vulnerable to competition over services. Therefore KS uses leasing to 1. prevent resale of it’s (used) technology and to 2. build switching costs against entrants into the services segment.

To the first point note that KS faces no other software competition in this segment so it is particularly interested in forestalling competition from itself. With regard to point 2. KS faces competition over services so it uses leasing to create barriers to entry. Leasing network cards as opposed to selling them outright creates switching costs for the lessee if they move to a new services vendor in the form of three work days per computer. The desire to avoid switching costs makes customers willing to pay more for KS’s services than they would to a competitor of KS.

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SUGGESTED ANSWERS TO THE CASE QUESTION: Question #14 Part a (I)

1. Suppliers

2. Buyers (Retailers)

2. Buyers (Consumers)

4. Substitutes 3. CompetitorsCompany

5. BTE

Commodities: sugar, grains etc. not dangerous

•Breakfast bars/sweets•Fruit/yogurt/healthy stuff•Coffee Shoppe foods/prepared food•Skip breakfast

Based on price realization of cereal (7%) vs. all food at home (13%) and the CPI (17%) substitutes appear to be gaining on cold cereal

Mfg. and marketing scaleBrandFew technological barriers

Market only growing 1%

See next page for details

2 segments: sugar & healthy

Generally ignored in the case but we know they are growing more powerful

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SUGGESTED ANSWERS TO THE CASE QUESTION: Question #14 Part a (II)

Player

Quaker

Ralston Purina

Kellogg

General Mills

General Foods

Other

3. Competitors

1987

8%

6%

41%

21%

13%

11%

1990

7%

6%

39%

24%

11%

13%

Change

+1%

-

-2%

+3%

-2%

+2%

Comment/brand

Oats are growing

TMNT & licensing brandsCorn & Frosted Flakes, Raisin Bran etc.

Cheerios and extensions

PL is growing, eroding price realization

note: 1% market share is worth $70 million in revenue . . . so the change in Kellogg’s market share is significant

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SUGGESTED ANSWERS TO THE CASE QUESTION: Question #14 Part b

The category is barely growing in spite of the fact that real price realization has been falling. Furthermore, Kellogg is losing market share. As the #1 player (think Stackelberg) it looks like Kellogg reduced prices less than it’s competitors because it needs to “reset” the category price equilibrium at a lower price point to increase category growth. Furthermore, Kellogg appears to be reducing its price realization relative to it’s direct competitors to increase market share in the short run . . . perhaps in the hope that it can retain some of these customers once competitors respond.

Cereal brands are somewhat differentiated but price is clearly a major factor in the consumer calculus. Therefore, Kellogg’s “defection” from the well established oligopoly game is likely to lead to price cuts from competitors in the next “round.”

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SUGGESTED ANSWERS TO THE CASE QUESTION: Question #14 Part c

The fact that the market leader is competing on price in an industry where the oligopoly game is well established is a bad sign for the cold cereal industry since it implies that profits are at an unsustainable level.

Innovate in new categories: A happier solution for all players would be for Kellogg to innovate, perhaps by developing new products that address new trends in breakfast consumption behavior (e.g., breakfast bars), to increase intrinsic demand for its cold cereal. Extending its products into competing categories might also allow Kellogg to play the oligopoly game across categories.

Brand development within category: 1. One weakness in Kellogg’s cereal portfolio is in oats so introducing an oat brand is obvious strategy to consider. 2. General Mills has been growing faster than the category through brand extensions. This may also be a good strategy for Kellogg.

Cost cutting is another “obvious” strategy. The problem with cost reduction is, of course, that it doesn’t help increase demand -- the central issue here.

Other marketing maneuvers could be productive here. For example reducing spend on promotions of legacy brands in favor of brand building activities like advertising and new product promotion.