PART II OLIGOPOLY
II. 2 COLLUSION
Σ Π (oligopoly) < Σ Π (monopoly)
→ Externality: i Max Π
iat the expense of Π
j, j ≠ i.
→ Why not make a deal to increase market power?
→ Collusion: one way available to firms to increase market power … at consumers’
expense.
→ * Either official (i.e. cartel)
example : oil price increases in 1973 by OPEC
* Or, more frequently, secret because illegal by the Sherman Act (US) and by
article 85 of the Treaty of Rome (EU).
→ Collusion is frequently a secret agreement either on prices or on quantities (as in the present chapter).
Instead, firms can also agree on advertising expenses, territory sharing, quality,
etc.
example of territory sharing: the chemical industry in the 20s
ICI → UK & Commonwealth
German firms → continental Europe Du Pont → America
Illegal since then.
II. 2. 1. Repeated interaction and stability of collusive agreements
Signing a collusive agreement does not seem to be an indivual best reply strategy
→ deviations, instability? Introduce dynamics
qA
qB
qM
qM
The Model
• Cf. Bertrand (duopoly, homogeneous product, constant and symmetric MC, no capacity constraint)
• Many periods (t = 1, 2, …)
• Firms can change their prices
• Bertrand game at each period: Firms play a repeated game
Equilibrium of such a dynamic game?
• The well-known Nash-Bertrand static equilibrium can be an equilibrium in this dynamic setting
• There can be other equilibria
• Consider the following tit-for-tat strategy
and equally share Π
Mbetween firms
Nash equilibrium?
- If no firm deviate from P
M, each firm obtains the following benefits
where δ is the time-discount factor.
It represents the degree of patience of a firm (patience high if δ close to 1)
- Simplifying:
- Alternatively, if a firm unilaterally deviates from P
M, it obtains the following profits:
- Collusion with P
i= P
M, i = A, B, is a Nash equilibrium if
- The importance of the discount factor, δ .
It measures what $1 is worth in the future compared with what it is woth today.
Generally, we assume that 0 < δ < 1.
- Why δ < 1?
Opportunity cost of time:
$1 today = $(1+r) tomorrow, where r = interest rate.
→ $1 tomorrow is worth $ today
→
Factors influencing the stability condition for a collusive agreement:
* n : number of firms → condition :
€
δ ≥1− 1 n.
* f : frequency of interactions between firms, frequency of price settings (annual).
When f is higher, the future is closer.
* r : annual interest rate → : periodical rate →
* h : probability to be active on this market next period (obsolescence, ARV versus curative vaccine).
* g : demand growth rate
→ stability condition:
€
δ = h(1+g) 1+ r
f
≥1− 1 n