A
Stackelberg Price Leadership Model
with Application to Deregulated Electricity Markets
Z. Yu
(IEEEl Member),
F.T.
Sparrow,
T.L. Morin, G. Nderitu
Institute for Interdisciplinary Engineering Studies
Room
334,1293
Potter, Purdue University
West Lafayette, IN
47906,
USA
Email:
z
yu
@
ecn
.
purdue
.
edu
Abstract

This paper presents a Stackelberg price
leadership model for simulating deregulated electricity
markets consisting of one or a few large producers and a
larger number of fringe producers. It is assumed that the
large producer(s) would adopt oligopoly strategy using
their market power while the small producers would use
Bertrandlike
strategy. The model is
a
multiobjective
profit maximization program. The multiobjectives are
converted into the same number of partial Lagrangian
functions with power production and supply as the
control variables.
A
set of KKT conditions is then
derived considering
the game strategies of
the
producers. Test results show that the model successfully
produces a total profit that is greater than the profit from
a welfare maximization model but is less than that from
a collusion model. Producers who adopt Cournot
strategy are better off with higher profits as compared
with marginal cost pricing.
Keywords

Stackelberg model, price, deregulation,
electricity, gaming, welfare, profit.
I.
INTRODUCTION
The general formulation of imperfect competition may
be described by a socalled conjectural variations model
(CVM) [page 645.11 as follows:
WS)
ads)

=
0,
V
S.
Or
equivalently,
n(S)
is the profit of producer
S,
q(S)
is the supply
quantity by S, P is market price,
MC[S,
q(S)]
is the
marginal cost of
k
represents producers other than
One way to solve
this
CVh4 model is to use the
Stackelberg method. In the method, it is assumed that
the market in question is composed of a single price
leader and a fringe of quasicompetitive producers. In
paper, we further assume that the leader is also a
large producer with
a
large market share who would
adopt Cournot strategy[l, 2, and 31. We also assume
that the fringe producers would adopt competitive
pricing strategy, which could be described
as
Bertrand
like
strategy
[l,
41.
That is, the fringe producers bid
their marginal cost functions. Further, it is assumed that
the total supply of the fringe producers is insufficient
for the whole market
so
that the leader will have
room
tcl play its strategy. This setting can be easily extended
tcl the case where a few large producers dominate the
market subject to the strategy of some fiinge producers.
Traditionally, the price leadership model is solved
in two parts: a master problem for the leader and a sub
problem for the fringe producers [5, 61. Iteration is
cimied out between the two problems and convergence
is usually guaranteed for “wellbehaved” problems.