Game Theory The Competitive Dynamics of...
Transcript of Game Theory The Competitive Dynamics of...
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BUSA 4800/4810 Feb 23, 2012
• Topics:
– Midterm Exam
– Non-cooperative Duopoly
– Best Response and Solver
– Airbus Project
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Midterm, March 5 • Theory Section and Case Study
• Theory:
– Lecture Notes & associated chapters
– Porter Articles
– Game Theory (questions online)
• Case: Danmark Packaging
– Prep/stud Question posted
– 2 or 3 of posted questions on exam
– 1 question will be NEW
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Cournot Duopoly Model
• Consider a market with two large firms who compete for market share
• Assume that they produce a homogeneous good
• Examples: – Concrete Industry
– Pulp and Paper Mills
– Steel Industry
– Industrial Chemicals
• These types of industries produce goods that are inputs into other product markets
• Therefore there will be a single price for output of both firms
• Market price is determined by total quantity available
• Quantity (or capacity) of each firm will be the strategic choice variable
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Profit Maximization ( 1 firm)
• Demand function
– Q = 10 – P
• Total Revenue:
– TR = PxQ
• Costs:
– $4 per unit
– TC = 4Q
Price Quantity
Total
Rev
Total
Cost Profit
10 0 0 0 0
9 1 9 4 5
8 2 16 8 8
7 3 21 12 96 4 24 16 8
5 5 25 20 5
4 6 24 24 0
3 7 21 28 -7
2 8 16 32 -16
1 9 9 36 -27
0 10 0 40 -40
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Profit Max Graphically
10
1053
7
4
6
MC = 4
MR D
Quantity
9 profit
PRICE
10
1053
21
12
6
TC = 4q
TR = pxq
= (10-q)q
quantity
9 profit
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Cournot Best Response Functions
•Firm 1’s Response
•If firm 2 doesn’t produce, act like a monopoly
•Or if q2 = 0, q1 = 3
•If firm 2 “floods” the market, then don’t produce
•Or if q2 = 6, q1=0
•1’s response “Function”
•q1 = 3 – 0.5q2
•Firm 2’s Response
•q2=3 – ½q1
3
6
q2
63 q1
2
2
Cournot
Firm 1's Best Response
Firm 2's Best
Response
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Airbus 2012 • Form Teams
• Read Airbus Case
• Complete the Excel Spreadsheet
– Fill in missing values
– Add additional sheets for each scenario
• Write a Formal Report with
– Overview of the situation
– Explanation of values used
– Results and recommendations (with defendable analysis)
– Sensitivity Analysis (What if’s)