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which shows that information about the current price elasticity of demand is suf-
ficient to obtain such an estimate. In practice, price experiments are commonly
carried out by firms through price discounts, hence this information is usually
readily available.
Notice that (5.48) is not a linear approximation of f ,asfirmk neglects the
influence of the competitor's production in the computation of the expected price.
Needless to say that this is a very rough approximation. However, this might not
be far from reality, as many authors point out (see for example Kirman (1975)).
Moreover, as we shall see below, even if in the computation of the expected price the
firms neglect the influence of competitors' outputs, the dynamic process generated
by such an adjustment procedure may lead to convergence to the same equilibria as
the best reply dynamics.
If firm k uses (5.48) to compute the expected price, the expected profit for the
next time period is approximated by
x
k
.t
C
1/
f.Q.t//
C
f
0
.Q.t//.x
k
.t
C
1/
x
k
.t//
C
k
.x
k
.t
C
1// .k
D
1;:::;N/;
and the optimal response of firm k, under this information set, is computed as
R
k
.Q
k
.t/;x
k
.t//
D
arg max
x
k
0
˚
x
k
f.x
k
.t/
C
Q
k
.t//
C
f
0
.x
k
.t/
C
Q
k
.t//.x
k
x
k
.t//
C
k
.x
k
/
(5.51)
for k
D
1;:::;N. By assuming a positive optimum, the first order condition implies
that
f.Q.t//
C
2f
0
.Q.t//x
k
f
0
.Q.t//x
k
.t/
C
k
.x
k
/
D
0.k
D
1;:::;N/: (5.52)
These first order conditions, computed at the equilibrium, are the same as the first
order conditions obtained for the Cournot game with perfect knowledge of the price
function f . Consequently, the steady states of the optimization problem with local
monopolistic approximation are also Cournot-Nash equilibria of the Cournot game
with complete knowledge of the price function. It is important to point out that this
distinguishes the oligopoly models based on LMA from the oligopoly models with
misspecified demand functions, which we have considered in the previous section
of this chapter. Whereas with misspecified demand functions the steady states are no
longer Nash equilibria of the true game, in the case of LMA the repeated decisions
of boundedly rational players who do not know the global shape of the demand func-
tion may lead to convergence to a Nash equilibrium. Of course, the more refined the
decision-making process and the corresponding decision rule, the more expensive it
is likely to be to obtain data for such a rule. Therefore, especially when a (single)
decision is not of crucial importance, no more than an approximate solution may be
justified. Some authors denote such decisions which are based on simple and inex-
pensive computations as “optimally imperfect decisions” (see for example Baumol
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