Oligopolio

ARTICLE IN PRESS

Journal of Economic Theory 114 (2004) 231–254

Coalition-proof supply function equilibria in
oligopoly
Juan Delgadoa,b and Diego Morenob,Ã
a

European Commission, Competition Directorate-General (J70/2/110) Post, Telecommunications and
Information Society Co-ordination, B-1049 Brussels, Belgium
b
Departmento de Economı´a, Universidad Carlos III de Madrid, 28903,Getafe, Spain
Received 6 March 2001; final version received 12 November 2002

Abstract
In an industry where firms compete via supply functions, the set of equilibrium outcomes is
large. If decreasing supply functions are ruled out, this set is reduced significantly, but remains
large. Specifically, the set of prices that can be sustained by supply function equilibria is the
interval between thecompetitive price and the Cournot price. In sharp contrast, when
the number of firms is above a threshold we identify (e.g., three if demand is linear), only the
Cournot outcome can be sustained by a coalition-proof supply function equilibrium.
r 2003 Elsevier Science (USA). All rights reserved.
JEL classification: C72; D43; L13; L51
Keywords: Oligopoly; Cournot; Competition via supply functions;Coalition-proofness

1. Introduction
We study an oligopoly where firms compete via supply functions. In this setting,
each firm chooses a supply function. The supply functions of all firms are then
aggregated to form the market supply which, together with the market demand,
determine the market clearing price and the production of each firm. This model of
competition describes many markets morerealistically than the Cournot or the
Bertrand models. In markets for government procurement contracts, or in the
Ã

Corresponding author. Fax: +34 91 624 9875.
E-mail addresses: juan.delgado-urdanibia@cee.eu.int (J. Delgado), dmoreno@eco.uc3m.es
(D. Moreno).
0022-0531/03/$ - see front matter r 2003 Elsevier Science (USA). All rights reserved.
doi:10.1016/S0022-0531(03)00123-6

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J. Delgado, D. Moreno / Journal of Economic Theory 114 (2004) 231–254

recently deregulated electricity markets, for example, that the strategies of the firms
are supply functions is a feature of the institutional setting.
A shortcoming of this model is that the set of outcomes that can be sustained by
supply function equilibria (SFE henceforth) is very large—see, e.g.,Grossman [7],
Hart [8]. Klemperer and Meyer [10] have studied the consequences of introducing
demand uncertainty into the model, and have shown that if uncertainty is
unbounded there is a unique equilibrium. Unfortunately, in many markets demand
uncertainty plays a small role.
We study a version of the model where the strategies of the firms are restricted to
non-decreasing supply functions. Thisrestriction seems reasonable and may add
realism to the model: in many markets firms may not be able to commit to a
decreasing supply schedule; in others, decreasing supply functions are explicitly ruled
out by design. It turns out that restricting the strategy spaces significantly reduces the
set of equilibria—the monopoly price, for example, can no longer be sustained by
SFE. Nevertheless,the set of equilibrium outcomes remains large. Specifically, the
set of prices that can be sustained by SFE is the interval between the competitive
price and the Cournot price. Further, the prices in this interval can be sustained by
SFE leading to symmetric outcomes as well as by SFE leading to asymmetric ones.
(The Cournot price is the unique exception: every SFE leading to this price yieldsthe
Cournot outcome.)
Next, we consider a setting where firms can communicate prior to taking an
action, but cannot make binding commitments, and we study whether accounting for
the opportunities of coordinated action that communication brings about provides a
basis for determining which outcomes may arise. In non-cooperative environments
where players can communicate, equilibria are not...