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
Cartel stability in an infinitely repeated game
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
Detection and Fines
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
Experiment Cartel stability Antitrust policy
Leniency programs