Implicit Cartels 14.12 Game Theory Muhamet Yildiz 1 ~P ) ~ L - - PDF document

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Lecture 15 Implicit Cartels 14.12 Game Theory Muhamet Yildiz 1 ~P ) ~ L lgtl y ~h ~1t!:r1 ~ ~J! ~ Ji ~!i.ft ntr Inflation Adjusted Mon t hly CRUDE OIL PRICES (1946 p resent) In June 2010 Dollars C www .lnflationData.com Updated 7/ 21

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1

Lecture 15 Implicit Cartels

14.12 Game Theory Muhamet Yildiz

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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

Ji ~ ~J! ~ ~1t!:r1 y ~h lgtl ~ L

__ $40 Inflation Adjusted Oil Price $20

Nominal Oil Price -.

Source of Data: Oil Prices-

WMY.ioga.comiSpeciallcrudeoiLHist.htm CPI-U Inflation index- WMY.bls.gov

2

Courtesy of InflationData.com. Used with permission.

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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

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0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 20 40 60 80 100

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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.

D-

VOIC =
Equilibrium iff
~

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0.4

0.3 »0.2 0.1

x=8, y=(3-53 8Y(%)

0.4 0.6 0.8

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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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MIT OpenCourseWare http://ocw.mit.edu

14.12 Economic Applications of Game Theory

Fall 2012 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.