Chemistry Reference
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This further implies that the realized industry output at the subjective equilibrium
can be expressed as
A
N
A
k
A
!
X
kD1
Q
D
:
N
X
A
k
c
k
k
D
1
In Example 1.5 we determined the output of the industry in the full information case
as
.N
1/A
P
kD1
c
k
Q
D
:
It is important to realize that the quantities in the subjective equilibrium differ from
the quantities in the full information case. Of course, if A
k
D
A for each k,thatis
all firms know the true price function, then the expressions above coincide.
Oligopolies without full information have been examined by several authors.
Okuguchi (1976) investigated discrete time dynamic models without full infor-
mation, and his stability analysis was based on the contraction mapping theorem.
Szidarovszky and Okuguchi (1990) discussed the asymptotic properties of dynamic
oligopolies with perceived marginal costs. Kirman (1975, 1983), and Gates et al.
(1982) should also be mentioned as early contributions. Leonard and Nishimura
(1999) assumed that the firms know the shape of the demand function but they mis-
specify its scale. They show that if players (slightly) over- or underestimate the true
demand, then an adaptive process based on the best replies converges towards a
unique steady state that differs from the full-information (Nash) equilibrium. They
also demonstrate that this steady state may lose stability as the misspecification
error (of one firm) becomes larger. The general case has been briefly analyzed in
Szidarovszky et al. (2008) for the concave case.
In his early paper Kirman (1975) considers a simple duopoly model, where he
assumes that the duopolists are not aware that their demand depends on each other's
action. The players choose their quantities such that the expected profit of the next
period is maximized and the duopolists update their estimates of the parameters of
the (misspecified) perceived model. Within this simple framework, he shows that
instead of converging to the “true” situation, the beliefs of the agents may drive
the model towards some other outcome. In addition to the result that agents are
not able to learn the true equilibrium, it is also shown in Kirman (1975, 1983) that
if convergence to the full information equilibrium fails, the process may become
path dependent, that is the particular equilibrium that can be observed depends
on the starting conditions. Furthermore, Brousseau and Kirman (1993) find regions
of stability as well as complicated dynamics in their simulations, whilst Kirman
(1995) makes some remarks on basins of attraction. Schinkel et al. (2002) con-
sider an oligopolistic price setting model where firms do not know the market
demand but have demand conjectures instead. They analyze the global dynamics
and show that the particular equilibrium that is reached in the long run depends
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