WALMART

1
WAL-MART

• Wal-Mart Stores, Inc. is the largest retailer and
  the largest company in the world based on
  revenue.
• Wal-Mart was founded by Sam Walton in 1962. In
  the fiscal year ending January 31, 2005, Wal-Mart
  had US285.2 billion in sales and net income of
  10.3 billion (a 3.6 profit margin).
• Forbes magazine points out that if Wal-Mart were
  its own economy, it would rank 23rd in the world,
  with a GDP between Austria and Saudi Arabia. It
  is the largest private employer in the United
  States, Mexico, and Canada.
• It holds a 8.9 percent retail store market share
  in other words, 8.90 out of every 100 spent in
  American stores is spent at Wal-Mart. In 2004,
  cash donations to charities by Wal-Mart, its
  employees, and its customers made through
  Wal-Mart, the Wal-Mart Foundation and the Sam's
  Club Foundation totaled more than 170 million
  (less than 0.06 of Wal-Mart's gross revenue,
  less than 1.7 of profit).

2
Introduction

• In a wide variety of markets firms compete
  sequentially
• one firm makes a move
• new product
• advertising
• second firms sees this move and responds
• These are dynamic games
• may create a first-mover advantage
• or may give a second-mover advantage
• may also allow early mover to preempt the market
• Can generate very different equilibria from
  simultaneous move games

3
Stackelberg

• Interpret in terms of Cournot
• Firms choose outputs sequentially
• leader sets output first, and visibly
• follower then sets output
• The firm moving first has a leadership advantage
• can anticipate the followers actions
• can therefore manipulate the follower
• For this to work the leader must be able to
  commit to its choice of output
• Strategic commitment has value

4
Stackelberg Equilibrium an example
Both firms have constant marginal costs of 10,
i.e., c 10 for both firms

• Assume that there are two firms with identical
  products
• As in our earlier Cournot example, let demand be
• P 100 - 2Q 100 - 2(q1 q2)
• Total cost for for each firm is
• C(q1) 10q1 C(q2) 10q2

• Firm 1 is the market leader and chooses q1
• In doing so it can anticipate firm 2s actions
• So consider firm 2. Demand is
• P (100 - 2q1) - 2q2
• Marginal revenue therefore is
• MR2 (100 - 2q1) - 4q2

5
Stackelberg equilibrium (cont.)
Equate marginal revenue with marginal cost
This is firm 2s best response function
Solve this equation for output q2
But firm 1 knows what q2 is going to be
MR2 (100 - 2q1) - 4q2
q2
Firm 1 knows that this is how firm 2 will
react to firm 1s output choice
MR (100 - 2q1) - 4q2 10 c
From earlier example (slide 22) we know that
22.5 is the monopoly output. This is an
important result. The Stackelberg leader
chooses the same output as a monopolist would.
But firm 2 is not excluded from the market
?q2 22.5 - q1/2
So firm 1 can anticipate firm 2s reaction
Demand for firm 1 is
P (100 - 2q2) - 2q1
22.5
P (100 - 2q2) - 2q1
Equate marginal revenue with marginal cost
P (100 - (45 - q1)) - 2q1
S
11.25
? P 55 - q1
Solve this equation for output q1
R2
Marginal revenue for firm 1 is
q1
MR1 55 - 2q1
45
22.5
55 - 2q1 10
? q1 22.5
? q2 11.25
6
Stackelberg equilibrium (cont.)
Leadership benefits the leader firm 1 but harms
the follower firm 2
Aggregate output is 33.75
Leadership benefits consumers but reduces
aggregate profits
q2
Firm 1s best response function is like firm 2s
So the equilibrium price is 32.50
45
Firm 1s profit is (32.50 - 10)22.5
R1
Compare this with the Cournot equilibrium
? p1 506.25
Firm 2s profit is (32.50 - 10)11.25
22.5
? p2 253.125
C
We know (see slide 22) that the Cournot
equilibrium is
15
S
11.25
R2
qC1 qC2 15
q1
The Cournot price is 40
45
15
22.5
Profit to each firm is 450
7
Stackelberg and Commitment

• It is crucial that the leader can commit to its
  output choice
• without such commitment firm 2 should ignore any
  stated intent by firm 1 to produce 45 units
• the only equilibrium would be the Cournot
  equilibrium
• So how to commit?
• prior reputation
• investment in additional capacity
• place the stated output on the market
• Finally, the timing of decisions matters
• But is moving first always better than following?
• Consider price competition
• If products are differentiated, price competition
  gives a second mover advantage.

8
Dynamic games and credibility

• The dynamic games above require that firms move
  in sequence
• and that they can commit to the moves
• reasonable with quantity
• less obvious with prices
• with no credible commitment the solution of a
  dynamic game becomes very different
• Cournot first-mover cannot maintain output
• Bertrand firm cannot maintain price
• Consider a market entry game
• can a market be pre-empted by a first-mover?

9
Credibility and predation

• Take a simple example
• two companies Volare (incumbent) and MyAir
  (entrant)
• Newvel makes its decision first
• enter or stay out of Volares market
• Volare then chooses
• accommodate or fight
• pay-off matrix is as follows

10
An example of predation
What is the equilibrium for this game?
But is (Enter, Fight) credible?
The Pay-Off Matrix
There appear to be two equilibria to this game
Volare
(Enter, Fight) is not an equilibrium
Fight
Accommodate
(Stay Out, Accommodate) is not an equilibrium
(0, 0)
Enter
(0, 0)
(2, 2)
MyAir
(1, 5)
Stay Out
(1, 5)
(1, 5)
11
Credibility and predation 2

• Options listed are strategies not actions
• Volares option to Fight is not an action
• It is a strategy
• Volare will fight if MyAir enters but otherwise
  remains placid
• Similarly, Accommodate is a strategy
• defines actions to take depending on MyAirs
  strategic choice
• Are the actions called for by a particular
  strategy credible ?
• Is the promise to Fight if MyAir enters
  believable
• If not, then the associated equilibrium is
  suspect
• The matrix-form ignores timing.
• represent the game in its extensive form to
  highlight sequence of moves

12
The example again
What if MyAir decides to Enter?
Fight is eliminated
Volare is better to Accommodate
(0,0)
(0,0)
Fight
Fight
(2,2)
Accommodate
Enter
V2
Enter
(2,2)
Enter, Accommodate is the unique equilibrium
forthis game
MyAir
MuAir will choose to Enter since Volare will
Accommodate
M1
Stay Out
(1,5)
13
The chain-store paradox

• What if Volare competes in more than one market?
• threatening in one market one may affect the
  others
• But Seltens Chain-Store Paradox arises
• 20 markets established sequentially
• will Volare fight in the first few as a means
  to prevent entry in later ones?
• No this is the paradox
• Suppose Volare fights in the first 19 markets,
  will it fight in the 20th?
• With just one market left, we are in the same
  situation as before
• Enter, Accommodate becomes the only equilibrium
  
• Fighting in the 20th market wont help in
  subsequent markets . . There are no subsequent
  markets
• So, fight strategy will not be adapted in the
  20th market

14
The chain-store paradox 2

• Now consider the 19th market
• Equilibrium for this market would be Enter,
  Accommodate
• The only reason to adopt Fight in the 19th
  market is to convince a potential entrant in the
  20th market that Volare is a fighter
• But Volare will not Fight in the 20th market
• So Enter, Accommodate becomes the unique
  equilibrium for this market, too
• What about the 18th market?
• Fight only to influence entrants in the 19th
  and 20th markets
• But the threat to Fight in these markets is not
  credible.
• Enter, Accommodate is again the equilibrium
• By repetition, we see that Volare will not
  Fight in any market