Avoiding the Bertrand Trap II: Cooperation

1
This Session

• Monopolistic competition Network externalities
• Decisions under uncertainty Auctions
• Classifying auctions
• Optimal bidding strategies
• Revenue equivalence
• Winners curse

2
Understanding Cost (session 3)
Revenue Understanding Demand (session 2)
Profit Revenue Cost
Pricing
Monopoly Trade off b/w high P and low Q
(session 6)
Perfect Competition Supply and entry decisions
(session 4 5)
What if we can price discriminate? (i.e.,
different consumers pay different
prices) (session 9 10)
How pricing depends on demand through the
elasticities (session 7)
Strategic Competition Solving for the NE
price and quantity competition (session 12)
How timing matters Stackelberg (session 14)
Exotic topics Strategic Demand Network
externalities and Auctions. (session 15)
Tools Games Theory (session 11)
Externalities and Strategic interaction
Collusion (session 13)
3
Monopolistic competition

• Barriers to entry caused by brand name, RD cost,
• first copy cost
• Free entry
• Cannot be perfect competition AC gt MC, Price
  must have mark up over MC.
• To have some market power
• Differentiated products
• Cournot (capacity) competition
• Small number of producers ? Oligopoly
• Large number ? Monopolistic Competition

Recall Nynex phone books
4
Monopolistic competition (cont.)

• Several firms with some market power
• More Realistic
• Examples games for play stations, vendors in
  fast-food court,
• coffee place, hairdressers

Duopoly
Market
Monopoly
5
Monopolistic competition (cont.)

• Several firms with some market power
• More Realistic
• Examples games for play stations, vendors in
  fast-food court,
• coffee place, hairdressers

Duopoly
Market
Monopoly
6
Pricing and RD costs
Lets try it again, this time using the insights
from monopolistic competition Q Why are you
charging so much for your product (e.g.,
drugs) A Because we have to recover RD
expenses.
7
Example
Number of firms Price
FC 1,000,000 FC 350,000
2 40
6 22.86
8
An Increase in Demand may cause market price to
fall!
Suppose FC 800,000
Number of firms Price
D1 D2
4 28
6 22.86
9
Monopolistic competition and network externalities
A source of network externalities?

• Network Externalities Defined Each consumers
  valuation increases
• if the numbers of other consumers using the same
  product goes up.
• Examples PC system using software application
  and add-on hardware, play station
• using games.

• Higher demand ? More firms (more varieties)?
  Lower prices ? Higher demand
• If the numbers of other consumers using the same
  product goes up, the prices
• are down and there are more varieties. Thus each
  consumers valuation increases.

10
Network Externalities

• Question Why is Microsoft so powerful?
• Deeper Question Why is demand inelastic and
  barriers high?

• Microsoft has a monopoly due to patent on Windows
  (but there are other monopolies around)
• Development costs are high (natural monopoly due
  to economies of scale but there is Mac, Linux)
• Microsoft is an industry standard
• Large user base means low per user costs, and
  many third party support products (tech-support,
  training, software).
• Switching costs Users accumulate Windows
  specific skills which makes it costly to switch
• Demand feeds into greater demand

Network Externalities
11
Network Externalities/Effects

• Network Externalities Defined Each consumers
  valuation increases if the numbers of other
  consumers using the same product goes up.
• Direct network effects telephones, email,
  languages.
• Indirect network effects computer operating
  systems (software), automobiles (servicing),
  banks (ATMs)

Fax Machines in the US
Fax introduced by ATT in 1925 but exploded from
10 to 95 of market from 1982 to 1987. First
e-mail sent in 1969, hardly used till 1989, since
then more than doubled every year.
6m
3m
0
1980
1970
1990
12
Markets With Network Externalities

• A customer makes a purchase decision based on
  her expectation of what others will do, and vice
  versa. Multiple equilibria are possible,
  depending on what people expect.
• Products must establish critical mass to
  survive. Once they take off, demand explodes
  (value increases with number of users) and it
  gives rise to lock-in.
• Creates entry barriers
• Examples
• eBay (profit margin 18 revenues increased by
  82 btw 2003-2004)

13
Path Dependence

• History matters.
• Accidents can determine winner
• QWERTY keyboards
• VHS vs. Beta

• Winner-take-all.
• Advantage to having one standard
• One product may takeover the entire market
• Natural monopoly but from increasing returns on
  demand side

For Thought Will the best standard/product/techno
logy always win?
14
Managerial Decisions Under Network Externalities

• Pricing strategies
• Keep in Mind
• For Microsoft and eBay, demand doesnt fall off
  even if competitors offer better products free.
• Demand is inelastic with respect to price - so
  the markup above MC can be massive.
• Considerations for Introducing New Products
• Dont underestimate the elasticity of demand
• If you cut prices demand rises by more than in
  absence of network externalities
• Dynamic pricing strategy is attractive start
  with a low initial price and increase it once you
  attract consumers
• First mover advantages exist since there are
  natural entry barriers
• Encourage or subsidize complementary goods if
  indirect network effects

15
Decisions Under Uncertainty Road Map

• Uncertainty about payoffs (Auctions)
• You want to sell a good to person with highest
  valuation but you cannot observe this
• And to give you a flavor of what you could learn
• Uncertainty about types (Adverse Selection not
  covered)
• You want to hire productive workers but
  productivity is not observable.
• You want to buy good quality products but quality
  is not observable (Buying a used car)
• Uncertainty about actions (Moral Hazard not
  covered)
• You want employees to work hard but effort is not
  observable

Incomplete information raises an additional
strategic consideration How to infer a players
private information from his action (as in
screening)
16
Auctions

• There are many buyers but just one good.
• Seller does not know buyers valuations.
• Buyer does not know other buyers valuations.
• Main idea Competition among buyers is used to
• get good allocated efficiently (to buyer with
  highest valuation)
• to extract the gains from trade for the seller.

Examples 3G Spectrum Auction Procurement
Auctions Internet Auctions Quota Rights
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Private vs. common value auctions

• TF1 is bidding for the broadcasting rights of
  FIFA World Cup 2002. You estimate that the
  approximate advertising revenue is 10 million
  euros.
• How high should you bid for a work of art which
  is worth to you 10,000 euros?
• How do you react if you find out someone elses
  valuation?

18
Classifying Auctions
Common Value Auction Unproven oil
fields Object has same value to all bidders but
each has only an estimate of the true value
Private Value Auction Van Gogh What others
know does Not affect your valuation
19
Auctions as games

• Players The n bidders
• Strategies How high to bid
• Payoffs A function of the bids For winner, it
  is the difference between his/her valuation and
  the price (which depends on bids). For loser it
  is zero.
• Incomplete information You know your valuation,
  v, but not the valuations of the other bidders

20
Classification of Auction Forms

• Simultaneous or sealed-bid.
• First-price (procurement contracts)
• Second-price (E-bay)
• Example
• Suppose bidder A bids 10, bidder B bids 15, and
  bidder C offers 20.
• First price Bidder C would win, pay his
  bid, namely 20.
• Second price Bidder C would win, pay second
  highest bid, namely 15.
• Sequential or open-outcry.
• English or ascending-bid. (art, wine)
• Dutch or descending-bid. (tulips treasury
  securities)

Sealed-bid first-price oral descending-bid
(Dutch) Sealed-bid second-price oral
ascending-bid (English)
21
The eBay auction format

• eBay was among the earliest to implement the
  novel proxy bidding auction format.
• Rules
• Bidders enter a proxy bid.
• This is a maximal amount their bidder elf will
  bid up to.
• Bidder elf automatically bids as needed to remain
  the high bidder up to the maximal amount entered.
• The winning bidder ends up paying an amount equal
  to the second highest bid (plus a bid increment)
• What form of auction is this? What should you
  bid??

22
Bidding Higher Than My Valuation in 2nd Price
Auction
Black true value Blue/dotted Competitors value
Case 1
Case 2
Case 3
No difference
No difference
Lose money
23
Bidding Lower Than My Valuation in 2nd Price
Auction
Black true value Blue/dotted Competitors value
Case 1
Case 2
Case 3
No difference
No difference
Lose money
24
Key Takeaway in 2nd Price Auctions

• Regardless of the other bidders strategies, the
  dominant strategy for me is to bid my value
• In these cases, the strategic sophistication (or
  lack thereof) on the part of the other players
  does not affect how to bid in the auction.
• It also means that figuring out the best strategy
  is not terribly complex.

25
Bidding in a First-Price Auction

• Bidding valuation get no surplus dominated
  strategy
• But bidding lower risks regret, i.e. losing when
  you have the highest valuation
• Optimal bid trades off risk of not winning vs.
  extra gain from winning with lower bid
• Shade bid shade less if many buyers
• (if 2 bidders bid Valuation/2. If N bidders bid
  (N-1)/NValuation)

26
Question In private auction, which Auction
Yields Higher Revenues on Average?

• Provided valuations are independent (no winners
  curse) and bidders are sophisticated learn to bid
  optimally then revenues in
• English Second Price First Price Dutch

27
Jar of Pennies Auction

• Actually there is 9.36 euros
• The winners are
• E1 Fabien for 83.2 euros or Milad
  for a bottle of champagne
• E2 Charles for 22.5 euros or Vaibhav for 25
  dollars (but two bids). Also David
  Young 4,500,000 dollars, Rodolpho Langostino!
• Lessons?
• Several bids at zero or negative numbers Type of
  auction?

28
An Acquisition Game
You are considering buying a firm from me. I know
the value of my company. You dont! You know
Value to me is uniformly distributed between 0,
100m Company is worth 50 more to you than it
is to me I am a lousy manager! You make me a
take-it-or-leave-it offer. What would you bid??
You may think On average company value to me is
50m So average company value to you is 1.550
75m So bid between 50m and 75m would be
profitable Is this reasoning correct?
29
Common Value Auctions The Winners Curse

• Examples
• Publishing Johnnie Cochrane Journey to Justice
  3.5M advance, 350,000 of 650,000 unsold.
• Offshore oil leases
• TBS paid 180m for Seinfeld reruns
• 3G Auctions in Europe
• Elective bidding

• General Result Bidder who wins pays the max bid
  
• ? Highest bid very, very likely to exceed the
  value of the good
• ? Winner is Cursed.
• Implications
• Bid more conservatively than in a private value
  auction

30
Wrap up on Auctions

• If seller and uncertain about valuations of
  buyers
• Design auctions to elicit information about
  valuations.
• Keep in mind Dutch 1st price English 2nd
  price
• In the long-run, on average 1st and 2nd price
  earn same revenues
• If buyer and in a common-value auction
• Beware of winners curse.
• Both buyer and sellers
• 2nd price auction Dominant strategy is to bid
  valuation
• 1st price auction Shade bid shade less if many
  buyers

31
Bidding in a First-Price Auction A Simple Example

• Suppose you have a value of 20 and are competing
  with one other bidder in a first-price auction.
  You need to choose a bid B to maximize your
  profits.
• You dont know the exact valuation of the other
  bidder (VC).
• But you do know that it is randomly drawn from 0
  to 100 (uniform distribution).
• Suppose you project that your rival will bid a
  constant percentage of his or her value. i.e,
  rival will bid aVc
• EProfit (20 B) Pr(B is the highest bid)
• What is Pr(B is the highest bid)?
• It is Pr(B Rivals bid) Pr(B aVc)

32
Bidding in a First-Price Auction A Simple Example

• I win whenever B aVC
• Equivalently, I win when
• VC B/a
• So Pr(B is the highest bid) becomes
• Pr(VC B/a) B/100a
• So now I need to choose B to maximize
• EProfit (20 B)(B/100a)
• Optimize by taking a derivative
• (1/100a) (20 2B) 0
• Or B 20/2 10 (shade bid)
• If my valuation equals V, bid V/2. Notice optimal
  bid does not depend on a
• (N-1) rivals Optimal bidding strategy is to bid
  a fraction (N-1)/N of my value.

Probability
0.01
100
B/a
Value