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

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 /20 10 $140 June 2008 Monthly Ave. Oil Price S125. 83in June 2010 Dollar s ---... Dec. 1979 Monthly Ave. Peak $120 $107.99 in June 2010 Dollars $1 00 -- --- -- - -- --- -- - -- --- -- --- -- ------ -- ------ -- - -- --- - - --- -- ------ -- ------ -- ------ -- - -- --- -- ---- $80 Nominal Peak $38 (Mo. Ave. Price) ____ __ $60 $40 Inflation Adjusted Oil Price $20 ••••••••••••••••••• Nominal Oil Price -. $0 Source of Data: O il Prices- WMY .i oga.comiSpecia ll crudeoiLHist.htm CPI-U Inflation index- WMY . bls . go v 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) = (n+1Y -1 • Equilibrium s: > 4n )2 u - ( 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

o ~ 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- VOIC = o o Equilibrium iff 7

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

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.