  We present a possible kind of generalization of the notion of ordered pairs
of cyclic maps and coupled fixed points and its application in modelling of
equilibrium in oligopoly markets. We have obtained sufficient conditions for
the existence and uniqueness of fixed (or best proximity) points in complete
metric spaces (uniformly convex Banach spaces). We get an error estimates of
the fixed (or best proximity), provided that we have used sequences of
successive iterations. We illustrate one possible application of the results by
building a pragmatic model on competition in oligopoly markets. To achieve this
goal, we use an approach based on studying the response functions of each
market participant, thus making it possible to address both Cournot and
Bertrand industrial structures with unified formal method. In contrast to the
restrictive theoretical constructs of duopoly equilibrium, our study is able to
account for real-world limitations like minimal sustainable production levels
and exclusive access to certain resources. We prove and demonstrate that by
using carefully constructed response functions it is possible to build and
calibrate a model that reflects different competitive strategies used in
extremely concentrated markets. The response functions approach makes it also
possible to take into consideration different barriers to entry. By fitting to
the response functions rather than the profit maximization of the payoff
functions problem we alter the classical optimization problem to a problem of
coupled fixed points, which has the benefit that considering corner optimum,
corner equilibria and convexity condition of the payoff function can be
skipped.
