Strategic Analysis of OPEC Market Power and Cartel Formation
Explore market power dynamics in OPEC through game theory models like Nash equilibrium and Stackelberg equilibrium. Analyze individual countries' incentives for production within the cartel.
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Presentation Transcript
YLE13: Duopoly Marko Lindroos
Research questions Market power and the formation of cartels (OPEC) Dynaamic game theoery models Nash equilibrium Stackelberg equilibrium(cartel leader, others followers) Stability? Individual countries in OPEC have an incentive to produce more
Duopoly Two identical firms, linear demand Max T rt b + ( ( ) ( )) ( ) e p q t q t q t dt 1 2 i 0 St = ( ) ( ) x t q t i i
Hamiltonian for firm 1 = + b ( ( ) ( )) ( ) ( ) ( ) p q t q t q t t q t 1 1 2 1 1 1
Maximum principle H 1 = 0 q 1 pb = 2 ( ) ( ) ( ) q t q t t 1 2 1 H 1 = ( ) ( ) t r t 1 1 x 1 rt 1) ( = t e 0
Timepath of costate variable Backstop-price at T is equal to shadow price (see previous conditions) pb = 1T ( ) ( ) be r t T 1) ( = t p
Reaction function ( ) b b r t T = 2 ( ) ( ) p q t q t p e 1 2 ( ) b r t T b + ( ) p e q t p 2 = ( ) q t 1 2
Extraction paths + ( ) b r t T b ( ) p e q t p = ( ) 1 q t 1 2 ( ) b r t T b 3 p e p = ( ) q t 1 2 2 b p ( ) r t T = = ( ) 1 ( ) ( ) q t e q t 1 2 3
Time of exhaustion rT b b 3 p p e d b + = p T x 0 d 2 r r
Price path b p = + = + ( ) b r t T ( ) ( ( ) ( )) 1 ( 2 ) p t p q t q t e 1 2 3
N firms + ) 1 ( ) b r t T b ( ( ) p e N q t p = 1 ( ) q t 1 2 ( ) b r T t b 1 N p e p ) 1 + = ( q 1 2 2 b p + ( ) r t T = = = = 1 ( ) ... q e q q 1 2 N ( ) 1 N rT b b + 1 p p e N n b + = p T x 0 n r r N
