Lecture 15
Implicit Cartels
14.12 Game Theory
Muhamet Yildiz
1
Inflation Adjusted
Mont hly CRUDE OIL PRICES
(1946·present) In June 2010 Dollars
C www.lnflationData.com
Updated 7/21 /2010
$140
$120
Dec. 1979 Monthly Ave . Peak
$107.99 in June 2010 Dollars
$1 00
-- --- -- - -- --- -- - -- --- -- --- -- --- --- -- --- --- -- - -- --- -
June 2008 Monthly Ave. Oil Price
---...
S125.83in June 2010 Dollars
- --- -- --- --- -- --- --- -- --- --- -- - -- --- -- ----
$80
Nominal Peak $38 (Mo . Ave. Price)
$60
$40
$20
____ )ntr~!i.ft~PJi~~~J!~~~~1t!:r1y~h lllgtl~L __
Inflation Adjusted Oil Price
•••••••••••••••••••
Nominal Oil Price - .
$0
Source of Data:
Oil Prices- WMY.ioga.comiSpeciallcrudeoiLHist.htm
CPI-U Inflation index- WMY.bls.gov
Courtesy of InflationData.com. Used with permission.
2
Road Map/Model
Model: Infinitely Repeated Cournot Oligopoly:
• n firms, MC
= 0;
• Zero marginal cost;
• p = max{1-Q,0};
Road map:
1. Monopoly Production for patient firms
2. Optimal Cartel production
3. Carrot and Stick Strategies
4. Price Wars
3
Monopoly Production
Strategy: Each is to produce q = 1/(2n); if
any firm defects produce q = 1/(1+n) forever.
• Vc
• Vo
=
=
• V(DIC)
=
• Equilibrium
~
(n+1Y -1
s: >
4n
u - (
)2
n+1
4n
4
0.95
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0.55
0.5
0
20
40
60
80
100
5
0.95
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0.55
0.5
o
200
400
600
800
1000
6
Optimal Production (n=2)
Strategy: Each firm is to produce q*; if anyone
deviates, each produce 1/(n+1) thereafter.
o Vc=
o
VD-
o
VOIC =
o
Equilibrium iff
o
~
7
x =8, y=(3-53 8Y(%)
0.4
0.3
»0.2
0.1
o
o
0.2
0.4
0.6
0.8
x
8
Carrot and Stick
• Produce % at the beginning;
• at any t> 0,
- produce % if both produced % or both
produced x at (-1;
-otherwise, produce x.
9
Price Wars
• (2007 Midterm 2, P3)
• Stage Game: Linear Bertrand Duopoly (c=O; Q=l-p)
• Strategy: n + I modes: Collusion, WI, W2, ... , Wn.
Game starts at Collusion. Both charge 112 in the
Collusion mode and p*< 112 in WI, ... , Wn. Without
deviation, Collusion leads to Collusion, WI leads to
W2, .. . , W(n-l) leads to Wn, and Wn leads to
Collusion. Any deviation leads to Wl.
10
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14.12 Economic Applications of Game Theory
Fall 2012
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