ECOS3025 Lecture Notes - Lecture 12: Tacit Collusion, Bertrand Competition, Discounting
27 Oct 2018
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ECOS3025 THE ECONOMICS OF REGULATION
1
WEEK 12: COLLUSION
CARTEL INCENTIVES
• Cartel: group of firms that act collectively to raise their joint profits by restricting output or raising price.
• Collusion: cooperation to improve joint payoffs (in oligopoly: to raise joint profits).
• Tacit / Implicit Collusion: behaving cooperatively without communication.
• Explicit Collusion: communicating with your rivals to collude.
• Price-fixing cartels are illegal in Australia: by raising price and decreasing output relative to a non-
cooperative outcome, this leads to welfare losses.
• Strong collective incentive to form a cartel: if firms cooperate, they could earn almost monopoly profits
otherwise they face competitive / Bertrand / Cournot profits.
• However, firms have an individual incentive to cheat, e.g. in Bertrand competition, if a firm undercuts
its rival, it can capture the whole market.
• The logic is similar to the Prisoners’ Dilemma – firms would like to coordinate on, for example, the
monopoly price, but firms have a powerful incentive to undercut.
• Cartel could solve incentive problem by threatening to retaliate or punish if their rival undercuts. For
this, need patient firms who interact repeatedly.
REPEATED GAMES
• If firms interact repeatedly, they can condition output or prices on the past actions of their rivals,
allowing explicit or implicit threats and promises.
• When deciding whether to cheat or cooperate, firms weigh the immediate gains from cheating (higher
current profits) and the future losses due to punishment.
• Grim Trigger Strategy: value of game in period
!
:
"#$%#&'%#() &'*%#(* &+$ ,-
)./
• Suppose both players play trigger strategies. Check for incentive to deviate by calculating values of
game if collude (with trigger strategies) –
"0
– and if defect (by cheating) –
"1
and let
"02"1
to find
'
to find value of discount factor that ensures that there is no incentive to deviate (cheat).
• Patience determines the viability of collusion – can cooperate if sufficiently patient.
PRICE COMPETITION COLLUSION
• Example: Two firms produce identical products. Each period over an infinite horizon, they
simultaneously set prices. Each firm has a constant marginal cost of
3
and no fixed costs. Suppose the
monopoly price is
45
. The firms consider the following grim-trigger strategies to collude:
4$
6
457897:;!<798=>?7?@!74$4578A7@B@=C74@=8;D74@=8;D
37;!<@=E8?@
If Firm 1 plays grim-trigger, he / she receives payoffs of:
"0$%0
F
G&'&'*&+
H
$%0
GI'$%5
JFGI'H
Firm 1’s most profitable deviation is to marginally undercut
45
. This yields payoffs of:
"1$%1&K
F
'&'*&+
H
$%5
Collusion is sustainable if
"02"1
à
,L
*F)./H 2%5
à
J
F
GI'
H
MG
à
'2)
*
• The sustainability of collusion in the Bertrand model does not depend on the collusive price.
o The critical discount factor
'N
is the same for any collusive price.
o Collusion and deviation profits are directly proportional to the collusive price.
• Corollary: equilibrium is not unique.
