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Chapter 28 Oligopoly Part I (Cournot competition (Nash equilibrium…
Chapter 28
Oligopoly
Part I
Oligopoly
A market structure with a small number of firms, such that each can influence market price wit its decision
The profits of each form will depend on its output choice and the output choices of competitors
A firm in an oligopolistic market will choose its quantity strategically
Game theory provides us with the tools to find the market equilibrium
Cournot competition
two firms compete by simultaneously choosing quantity
Firm 1's profits depend on its output choice q1 and its competitor's output choice q2
The first order condition will give a relationship between q1 and q2.
This is firm 1's
reaction function
or
best response function
: for any expected q2 chosen by the competitor, the function gives the q1 that will maximise firm 1's prodit
similar situations for firm 2
Nash equilibrium
Both players' chosen strategies are best responses to each other
In the Cournot duopoly, the Nash equilibrium q1
and q2
satisfy
That is, each firm is best responding to its competitor's quantity choice
Total quantity under Cournot duopoly is
• greater than under monopoly (and the price is lower)
• less than under perfect competition (and the price is higher)
Bertrand competition
two firms compete by simultaneously choosing price
Firm 1 has cost c1(q1)=cq1 and sets p1
Firm2 has cost c2(q2)=cq2 and sets p2
key assumption: the products of both firms are identical, so the firm that sets the lower price captures the entire market. And if p1=p2, the firms share the market equally
The Nash equilibrium is p1
=p2
=c
In equilibrium,
• both firms price at marginal cost
• the firms share the market
• the firms make 0 profit
Cournot $ Bertrand model choice
• markets in which firms
must commit to producing a certain quantity
before going to market may be modeled more accurately with
Cournot competition
• markets in which
quantity can be adjusted very easily
(e.g. digital products) may be modeled more accurately with
Bertrand competition
