lacks a convincing f oundation in oligopolistic markets and has to be
generalized to allow for the maximization of a more complex payoff function.
Also, from the classical contribution of Baumol (1959) it is customary to
argue that firms might be interested in objectives other than profits.
ii) On the other hand, in contrast with many contributions quoted above,
our approach does not rely on dynamics at all. This is not because the author
thinks that comparative statics can not profit from stability considerations
but because the actual dynamic processes which are used can hardly being
justified. Moreover, this stability conditions are usually very strong. For
instance in the Cournot model with linear demand and cost functions, the
equilibrium is unstable if the number of firms is greater than two. Thus, the
aim of the paper is to obtain the best possible results which depend only on
the aggregation axiom and the strong concavity condition.
Our results can be compared with those obtained under the (polar)
assumption of supermodularity. Roughly speaking, a game is Supermodular when
for each player her strategy set is the product of compact intervals and the
marginal profitability of any action increases with any other action of any
player (see Topkis (1979) for a more general definition). When strategy sets
are one-dimensional the above definition reduces to that of a game with
strategic complementarities (see Bulow, Geanakoplos and Klemperer (1985)). It
can be shown that if the marginal profitability of any action is increasing on
a parameter, say τ, (this is identical to our assumption 4), the largest and
smallest Nash equilibria are increasing functions of τ so if the Nash