Experiment Cartel stability Antitrust policy
Repeated games and cartel
Industrial organization – lecture 3
Experiment Cartel stability Antitrust policy
Benchmark
1. Write my price p ∈ {101, 102, 103, . . . , 110}.
2. Determine the market price pM = minimum of prices in the group.
3. Calculate the profit =
market price−100
number of group members with the same price (N)
if p = pM
0 if p > pM
Experiment Cartel stability Antitrust policy
Communication
1. Do you want to communicate/form a cartel? (fill in yes or no in column 1)
2. Reveal your answer sheets: If all yes – 1 minute of price negotiations.
Choice from {101, 102, 103, . . . , 110}. The price is not binding.
3. Write my price p ∈ {101, 102, 103, . . . , 110}.
4. Determine the market price pM = minimum of prices in the group.
5. Calculate the profit =
market price−100
N
if p = pM
0 if p > pM
Experiment Cartel stability Antitrust policy
Antitrust
1. Do you want to communicate/form a cartel? (fill in yes or no in column 1)
2. Reveal your answer sheets: If all yes – 1 minute of price negotiations.
Choice from {101, 102, 103, . . . , 110}. The price is not binding.
3. Write my price p ∈ {101, 102, 103, . . . , 110}.
4. Determine the market price = minimum of prices in the group.
5. Cartel is detected with 15% probability. Fine = 10 % of revenue.
6. Calculate the profit =



market price−100
N
− 0.1market price
N
if p = pM and you are in cartel and detected
market price−100
N
if p = pM and not in cartel or not detected
0 if p > pM
Experiment Cartel stability Antitrust policy
Leniency
1. Do you want to communicate/form a cartel? (fill in yes or no in column 1)
2. Reveal your answer sheets: If all yes – 1 minute of price negotiations.
Choice from {101, 102, 103, . . . , 110}. The price is not binding.
3. Write my price p ∈ {101, 102, 103, . . . , 110}.
4. Determine the market price = minimum of prices in the group.
5. If all say yes in 1., you may report the cartel for a cost equal to 1.
The 1st (no fine) and 2nd (50% fine) report will be chosen randomly.
6. If not reported, cartel detected with 15%. Fine = 10 % of revenue.
7. Calculate the profit =



market price−100
N
− 0.1market price
N
(0/0.5/1) if p = pM and cartel reported
market price−100
N
− 0.1market price
N
if p = pM , cartel and detected
market price−100
N
if p = pM , not cartel or not detected
0 if p > pM
Experiment Cartel stability Antitrust policy
One-shot or finitely repeated game
Pepall et al. (2014, pp. 349–361)
Simultaneous game:
• two firms 1 and 2
• each firm has two actions:
– cartel quantity qm
i
– Nash equilibrium (Cournot, Bertrand) quantity qn
i
• preferences given by profits of firms:
πd
i (default) > πm
i (monopoly) > πn
i (Nash) > πs
i (sucker)
Payoff matrix of the game:
firm 2
qm
2 qn
2
firm 1
qm
1 πm
1 ; πm
2 πs
1; πd
2
qn
1 πd
1 ; πs
2 πn
1 ; πn
2
Experiment Cartel stability Antitrust policy
Example – Cournot duopoly cartel game
Experiment Cartel stability Antitrust policy
Cartel stability in an infinitely repeated game
Future profits multiplied by ρ = pR, where
• p is the probability that the cartel continues
• R is the discount factor
Grim trigger - two options:
1. If firm i chooses cartel quantity, cartel survives – its profit is πm
i .
2. If firm i deviates, it gets πd
i in the first round and πn
i in all future rounds.
When does grim trigger make the cartel stable?
The cartel is stable if
ρ > ρ∗
=
πd
i − πm
i
πd
i − πn
i
Experiment Cartel stability Antitrust policy
Detection and Fines
Pepall et al. (2014, pp. 370–377)
The same infinitely repeated game, but with antitrust – parameters:
• a – probability that the authority will investigate the cartel
• s – probability that it leads to successful prosecution
• F – fine if the prosecution is successful
What happens to the expected cartel profits? When is the cartel stable?
Expected profits of a firm in cartel:
• without autitrust:
Vm =
πm
i
1 − ρ
• with autitrust:
V a
m =
πm
i − asF + asρ
1−ρ
πn
i
1 − ρ(1 − as)
Even if the fine F = 0, the cartel is stable if
ρ > ρa
=
πd
i − πm
i
(1 − as)(πd
i − πn
i )
> ρ∗
Experiment Cartel stability Antitrust policy
Leniency
The same infinitely repeated game with antitrust, but with leniency:
We assume that each firm may adopt on of the three strategies:
1. Collude, Not Reveal – the expected profits
V C
NR =
πm
i − asF + asρ
1−ρ
πn
i
1 − ρ(1 − as)
2. Collude, Reveal – if
• there is no investigation – keep cartel: V1 = (1 − a)(πm
i + ρV C
R )
• there is investigation – stay in cartel until the end of the period and
then reveal and pay a reduced fine L < F: V2 = a(πm
i − L +
ρπn
i
1−ρ
)
V C
R = V1 + V2 =
πm
i − L +
aρπm
i
1−ρ
1 − (1 − a)ρ
3. Defect – the expected profits are
Vd = πd
i +
ρπn
i
1 − ρ
What are the possible equilibria? How does the equilibrium selection depend on
antitrust parameters a and s and on the leniency fine L?
Experiment Cartel stability Antitrust policy
Leniency programs