Transcript M`s payoffs - Faculty Directory | Berkeley-Haas

Overview of Experiment
• 2 Markets, A and B
• Each Market lasts for 6 rounds
• Each group plays 3 times in Market A and
3 times in Market B
• Each group is matched with another group
only once
• In each round, role is either Manufacturer or
Retailer
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Teck Ho
Overview of Both B2B Channel Markets
• Manufacturer’s marginal cost is 20
• Manufacturer either chooses a simple wholesale
price X (in Market A) or a quantity discount
contract: X, Y and Break (integers from 0 to 100) (in
Market B)
• X must be greater than Y (since it is quantity
discount contract) in Market B
• Retailer chooses to Accept or Reject the offer
• If Retailer Accepts, she chooses the Retail Price
• Retail Price chosen determines Quantity and payoffs
for both players
• If Retailer Rejects, round ends. Both players earn 0
points
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Teck Ho
Demand Facing the Retailer
• In both markets, Retailer sees a simple linear
demand
• Demand = 100 – Retail Price
• If retail price = 20,
demand = 100 – 20 = 80
• If retail price = 50
demand = 100 – 50 = 50
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Teck Ho
Market A: Computation of Payoffs
M’s payoffs
= [X-20]* QUANTITY
R’s payoffs
= [PRICE – X]*QUANTITY
Total Cost to Retailer
xQ
Q
QUANTITY
Quantity Q = 100 – Retail Price
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Teck Ho
Market A: Sample Linear Price Contract
Total Cost to Retailer
X = 45
2000
1000
20
Price 80
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45
55
QUANTITY
If Price = 80
M’s payoffs
= [45 - 20]*20 = 500
R’s payoffs
= [80 - 45] *20 = 700
If Price = 55
M’s payoffs
= [45 - 20] *45 = 1125
R’s payoffs
= [55-45] *45 = 450
Teck Ho
Market B: Computation of Payoffs
If QUANTITY < = BREAK,
M’s payoffs
= [X-20] * QUANTITY
R’s payoffs
= [PRICE-X] * QUANTITY
Total Cost to Retailer
X x Break
+ Y x (Q2- Break)
If QUANTITY > BREAK,
M’s payoffs
= [(X - 20) * BREAK]
+ [(Y-20) * (QUANTITY – BREAK)]
R’s payoffs
= [PRICE * QUANTITY]
– [X * BREAK + Y * (QUANTITY – BREAK)]
X x Q1
Q1
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Break
Q2
QUANTITY
Teck Ho
Market B: Sample QD Contract 1
If QUANTITY = 10 (< = 20),
M’s payoffs
= [50-20] * 10 = 300
R’s payoffs
= [90-50] * 10 = 400
Total Cost to Retailer
1750
X = 50
Y = 25
BREAK=20
If QUANTITY = 50 (> 20),
M’s payoffs
= [(50 - 20) * 20] + [(25-20) * (50 – 20)]=750
R’s payoffs
= [50 *50] – [50 * 20 + 25 * (50 – 20)] = 750
500
10
20
Price
90
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50
50
QUANTITY
Teck Ho
Market B: Sample QD Contract 2
If QUANTITY = 20 (< = 25),
M’s payoffs
= [45-20] * 20 = 500
R’s payoffs
= [80-45] * 20 = 700
Total Cost to Retailer
1825
X = 45
Y = 20
BREAK=25
900
20
Price 80
25
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60
40
If QUANTITY = 60 (> 25),
M’s payoffs
= [(45 - 20) * 25] + [(20-20) * (60 –25)] = 625
R’s payoffs
= [40 *60] – [45 * 25 + 20 * (60 – 25)] = 575
QUANTITY
Teck Ho
Deciding the Winner
• Each group’s total earnings is the sum of its earnings either
as a manufacturer or a retailer in all six decision rounds
• The group who has the highest total earnings will win a
prize of
$40 (Ho & Ho Foundation) + $5 / Group = $100
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Teck Ho
Simple Rules to Follow
• In each decision round, manufacturers and
retailers will be given 5.5 and 3.5 minutes to make
their decisions respectively and --a prompt will
appear when the time limit expires
• Do not click on the BACK button on the browser
to return to a previous page--make sure the value
you entered in the decision box is correct before
clicking on the CONTINUE button.
– Clicking on the BACK button to enter a new value will
not work and may cause the system to behave
erratically
March 25, 2006
Teck Ho
Experiment Starts Here
http://128.32.67.154/contractdesign2/
March 25, 2006
Teck Ho
Steps in Designing B2B Contracts
• Figure out the maximum possible pie
• Choose a contract structure that makes the maximum
pie achievable (linear versus quantity discount (QD))
• Pick the right parameters to achieve the maximum pie
(Linear: X; QD: X, Break,Y)
• Pick the right parameters to divide the pie based on
relative bargaining power (Linear: X; QD: X, Break,
Y)
• Ensure voluntary and incentive-compatible
participation (i.e., retailers will choose the “right
way”)
March 25, 2006
Teck Ho
What is the Maximum Pie?
• Suppose manufacturer and retailer work as
a team (marginal cost = 20)
• Profits are:
(Price – 20)*Quantity = (Price – 20) x (100 – Price)
• Optimal retail price is 60 and quantity = 40
• Profits = 1600
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Teck Ho
Joint Decision: Optimal Retail Price
Sales
Quantity
Quantity = 100 - Price
40
$20
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$60
Teck Ho
$100
Price
Which Contract Form?
• Linear Wholesale Price Contract
• Nonlinear Whole Price Contract
– Block tariffs
March 25, 2006
Teck Ho
Linear Wholesale Price Contract
• Suppose Manufacturer offers Retailer a linear wholesale price
X. Marginal Cost is 20.
• Demand is: Quantity = 100 – Price
• Manufacturer’s profits = (X-20) * (100 – Price(X))
• Retailer’s profits = (Price – X)* (100 – Price)
• Optimal Decisions:
– Price(X) = (100 + X )/2
– X=60, Price=80, Quantity = 20
– M’s profits = 800, R’s profits = 400
– Total profits = 1200
• Total profits are 75% of the maximum possible profits (1600)
• Can Quantity Discounts Schemes Increase the Pie?
March 25, 2006
Teck Ho
Independent Channel Members
Manufacturer
20
X
Retailer
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Teck Ho
Price
Quantity=100-Price
Linear Pricing Contract:
Optimal Retail Price:
Sales
Quantity
Quantity = 100 - Price
100
- Price (X)
$X
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Price (X)
= ($100 + X)/2
Teck Ho
$100
Price
How to Achieve Maximum Pie?
• Marginal cost to the retailer = 20
• Optimal retail price = 60
March 25, 2006
Teck Ho
Market B: Optimal Design
• Choose X and Break
to divide the pie
Total Cost to Retailer
Y=20
X x Break
+ Y x (Q2- Break)
• Manufacturer makes
(X-20)*Break
X x Q1
Q1
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Break
Q2
QUANTITY
Teck Ho
Market B: Optimal Design
If QUANTITY (< = 32)
Price >= 68, Optimal Price = 72.5
M’s payoffs
= [45-20] * 27.5 = 687.5
Total Cost to Retailer
R’s payoffs
= [72.5-45] *27.5 = 756.25
X = 45
Y = 20
BREAK=32
If QUANTITY (> 32)
Price < 68, Optimal Price = 60
M’s payoffs
= [(45 - 20) *32] + [(20-20) * (40 –25)] = 800
R’s payoffs
= [60 *40] – [45 * 32 + 20 * (40 – 32)] = 800
32
March 25, 2006
QUANTITY
Teck Ho
Market B: 2-Block Tariffs
• Manufacturer sets Y = 20 to achieve the maximum pie
• Retailer chooses Price = 60, Quantity = 40
• Manufacturer chooses X and Break to divide the pie
based on the relative bargaining power
• Manufacturer earns (X-20)*Break leaving Retailer 1600
– (X-20)*Break
• A possible optimal contract:
– X=45, Y=20, Break = 32 (or X = 60, Y=20, Break=20)
– M’s Profits = 800, R’s Profits = 800, Total = 1600
March 25, 2006
Teck Ho
Summary
• Figure out the maximum possible pie!
• Choose a contract structure and the right parameters to
achieve the maximum pie
• Divide the pie based on bargaining power
• Ensure voluntary and incentive-compatible
participation (it is the interest of the retailer to choose
accordingly)
March 25, 2006
Teck Ho