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Bertrand’s model of oligopoly Strategic variable price rather than output.

  • Single good produced by n firms

  • Cost to firm i of producing qi units: Ci(qi), where Ci is

nonnegative and increasing

  • If price is p, demand is D(p)

  • Consumers buy from firm with lowest price

  • Firms produce what is demanded

Firm 1’s profit:

π1(p1, p2) =

p1D(p1) C1(D(p1)) p 1 D ( p 1 ) C 1 ( 1 2 D ( p 1 1 2 ) )

0

if p1 < p2 if p1 = p2 if p1 > p2

Strategic game: players: firms e a c h fi r m s s e t o f a c t i o n s : s e t o f a l l p o s s i b l e p r i c e s e a c h fi r m s p r e f e r e n c e s a r e r e p r e s e n t e d b y i t s p r o fi t

7

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