1
Lecture 15 Implicit Cartels
14.12 Game Theory
Muhamet Yildiz
Inflation Adjusted Monthly CRUDE OIL PRICES (1946·present) In June 2010 Dollars
C www.lnflationData.com Updated 7/21 /2010
$140 June 2008 Monthly Ave. Oil Price
Dec. 1979 Monthly Ave . Peak S125.83in June 2010 Dollars ---... $120 $107.99 in June 2010 Dollars
$1 00 -- --- -- - -- --- -- - -- --- -- --- -- --- --- -- --- --- -- - -- --- - - --- -- --- --- -- --- --- -- --- --- -- - -- --- -- ----
$80 Nominal Peak $38 (Mo. Ave. Price)
____ $60 )ntr~!i.ft~PJi~~~J!~~~~1t!:r1y~hlllgtl~L __
$40 Inflation Adjusted Oil Price
$20 ••••••••••••••••••• Nominal Oil Price -.
$0
Source of Data: Oil Prices- WMY.ioga.comiSpeciallcrudeoiLHist.htm CPI-U Inflation index- WMY.bls.gov
2
Courtesy of InflationData.com. Used with permission.
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 - ( n+1 )2
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 V D--
o VOIC = o Equilibrium iff
o ~
7
0.4
0.3
»0.2
0.1
o o 0.2
x=8, y=(3-53 8Y(%)
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
MIT OpenCourseWarehttp://ocw.mit.edu
14.12 Economic Applications of Game TheoryFall 2012
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
Recommended