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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

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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

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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

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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

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Carrot and Stick • Produce % at the beginning;

• at any t> 0, - produce % if both produced % or both

produced x at (-1;

-otherwise, produce x.

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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.

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14.12 Economic Applications of Game TheoryFall 2012

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