part ii oligopoly ii. 2 collusion
TRANSCRIPT
Σ Π (oligopoly) < Σ Π (monopoly)
→ Externality: i Max Πi at the expense of Πj, 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
Nash equilibrium?
- If no firm deviate from PM, 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 PM, it obtains the
following profits:
- Collusion with Pi = PM , 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− 1n.
* 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+rf
≥1− 1n
→ Therefore, collusion is more likely/more stable
• the more interactions are frequent
• the higher the probability to stay on the market
• the higher the growth rate
• the lower the number of firms.
→ Examples for f :
• gas stations: f daily;
• tour-operators: f seasonnal;
→ collusion is easier for gas stations (faster detection of deviations and therefore
faster punishment)
→ Examples for h :
• pharmaceutical firms (ARV versus vaccine): collusion is difficult
• cement : collusion is easier
Observations of collusive agreements:
Not frequent in reality, even tough it is beneficial even in very adverse conditions:
If n = 100, r = 10%, and f monthly
Why?
• It is illegal;
• High turnover (low h) ;
• Collusive strategy that implies a permanent price war. However, all firms are
better of revising their strategies over time, it is not renegotiation-proof.
Therefore, the threat of a price war is not credible.
• When it is difficult to observe prices, secret deviations are possible and the
collusive agreement is less stable.
To sum up
What matters for the stability of the collusive agreement is the trade-off short-term
gains and long-term losses.
II. 2. 2. Price wars
Observation
Industry prices oscillate between high levels and low levels.
→ Contradicts the collusive stability condition
→ Extensions of the model
Secret price cuts and demand flucuations
Markets with huge clients (concrete or ships), negotiated prices, difficult to
identify price cuts.
Model 1
Each firm only observes its own demand, not the total demand.
If a firm’s demand is low, either its rival has secretly decreased its price, or the
total demand is low.
→ Punishment? (bad equilibrium)
or not? (bad incentive).
Model 2
Each firm observes total demand.
Gains from deviations are higher the larger the total demand.
→ A collusive agreement should specify common price decreases in periods of
high demand to desincentivate unilateral deviations (the gains associated to a
deviation are lower if prices decrease).
→ Counter-cyclical prices.
Empirically,
Both models seem relevant, depending on the sectors under analysis:
• Cement prices between 1947 and 1981 : counter-cyclical
• Ships built in Chicago the East Coast: pro-cyclical prices