Problems for the first seminar: Oligopoly
ECON4820 Strategic competition — Spring semester 2010
Solutions to the problems will be presented Wed 3 February 2010.
Please direct any questions to Geir B. Asheim (Room ES1152, Tel: 228 55498,
e-mail: g.b.asheim@econ.uio.no)
Problem 1 (Quantity competition with 3 firms)
Tirole Exercises 5.3
Problem 2 (Asymmetric costs and concentration index)
Tirole Exercise 5.7
Problem 3 (Asymmetric costs and collusion)
Tirole Exercise 6.5
Problem 4 (Best response functions under quantity competition)
Tirole Exercise 20
Problem 5 (Rationing rules)
Tirole Exercise 21
Problem 6 (Entry and competition)
(a) Two firms, i = 1, 2 produce a homogenous product and both have unit
cost equal to c. The strategy of firm i is to choose a price p1 ≥ c. The
revenue of firm i is




p1 (1 − p1 )



1
p (1 − p1 )
2 1





0
if p1 < p2
if p1 = p2
if p1 > p2
Show that p1 = p2 = c is a unique equilibrium
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(b) Consider now the following to-stage game. In stage 1, each firm decides
whether to enter or not. If a firm chooses to enter, it must pay a cost ε
that does not depend on the quantity it produces. In stage 2, the following happens: If only one firm has entered, then this firm is a monopolist
facing the inverse demand function p = 1 − q; if both firms enter, then
they play the game under part (a). Find the subgame-perfect equilibria
of this two-stage game.
(c) Would it matter for your answers under part (b) if we had assumed
instead that the two firms compete in quantities rather than price in the
second stage (so that a Nash equilibrium of the Cournot model is realized
in stage 2 if both firms enter).
(d) What conclusions can be drawn concerning the connection between price
competition and entry?
Problem 7 (Repeated interaction with imperfect monitoring)
Within the framework of the Green-Porter cartel model, explain the following paradox: When the discipline of the cartel has broken down, then it
is better for all parties to forget the past and resume their collusion rather
than undertaking mutual punishment. Still, Green and Porter assume that
the punishment is undertaken. Why do not the firms resume their collusion
at once?
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